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Quote from Segoth »

Actually this is going to be determined by timestamp. It's true that in both cases conversion is dependent on Urborg, however the same is true for Urborg. If Urborg is applied first and then conversion, conversion will turn it into a plains which will affect what Urborg would apply to (much the same way Blood Moon does when dealing with that interaction). So what we have here is a dependency loop, which means we revert back to timestamp order.

On further reflection, you are correct that there is a dependency loop: here, applying Conversion's effect first would "change the text or existence of" Urborg's effect (C.R. 613.7a), so the latter is likewise dependent on the former, therefore a dependency loop exists and timestamp order is used (C.R. 613.7b).

Magical Hack's effect is a text-changing effect (layer 3 [C.R. 613.1c]), so it applies before Urborg's and Conversion's effects (both of which are in layer 4 [C.R. 613.1d]). Therefore, Magical Hack's effect will apply even if Urborg loses its abilities due to Conversion's effect (which will happen in both cases [C.R. 305.7, 305.6]) (the rules that can change how effects are ordered apply only "within a layer or sublayer" [C.R. 613.6, 613.7]).

In the first case, the relevant effects read "Each land is a Mountain in addition..." and "All Mountains are Plains". In the second case, the relevant effects read "Each land is a Swamp in addition..." and "All Swamps are Plains". In both cases, Conversion's effect depends on Urborg's since both effects are in layer 4 and the latter changes what lands the former affects (C.R. 613.7a), (EDIT [after comment 6]: but not vice versa, since applying the former first doesn't "change the text or existence of" the latter or what it applies to) and the latter is not dependent on the former within the meaning of C.R. 613.7a, including because applying the former first doesn't "change the text or existence of" the latter or what it applies to, so the latter is applied before the former (C.R. 613.7b-c), and all lands will be Plains (and no other land types) in either case and generally won't have any abilities other than "T: Add W" (C.R. 305.7, 305.6). EDIT: In both cases, applying Urborg's effect first would change what lands Conversion's effect applies to (within the meaning of C.R. 613.7a).

EDIT: Struck out some parts of this post after comment 5 was posted, and reinstated them after comment 6 after I was shown to be originally correct. The important thing to keep in mind here is that C.R. 613.7 applies only if one of the effects is dependent on the other but the latter is not dependent on the former.
EDIT (Aug. 5): Clarification; added rule citation.
EDIT (Dec. 13, 2018): Correctness edit.
EDIT (Apr. 6, 2019): Add rule citations; clarification; correctness edit.

No. A creature doesn't become tapped just because it loses vigilance. Vigilance means only that the creature doesn't become tapped as part of declaring it as an attacker (C.R. 702.20b); nothing in the rules for that ability attaches any consequences to an attacking creature that loses it (C.R. 702.20).

EDIT (Apr. 13, 2021): Clarification.

1. Tokens can go to a player's graveyard (or anywhere else, including exile or a player's hand) like any other permanent (C.R. 111.6); it's just that they will cease to exist as a state-based action (roughly after a spell or ability resolves [C.R. 117.3b, 117.5]) after they do so (C.R. 704.5d). Indeed, whether an artifact is a token doesn't matter for the purposes of Syndicate Trafficker's ability or Marionette Master's second ability (C.R. 111.6).
2, 3. In general, a player can activate an ability as many times as he or she can pay its cost (C.R. 118.3). (The abilities you mention don't have restrictions within the meaning of C.R. 602.1b -- such as "Activate this ability only once each turn" -- and they aren't loyalty abilities as they have no loyalty symbol in their costs [C.R. 606.2, 606.3], so they are subject to the same rules for when they can be activated that apply to activated abilities in general [C.R. 117.1b].)
4. Turning a permanent face up using morph (not: "flipping" it or "morphing" it) is a special action (C.R. 702.36e, 115.1), not a spell or ability that goes on the stack (see also C.R. 405.6d), so other players can't cast a spell or activate an ability in response to it (C.R. 117.7).
5. No. While a player is activating the crew ability, other players can't respond with spells or abilities, including those that would remove the creature from the battlefield (C.R. 601.2a-i and 602.2a-b have no priority window until the spell is cast or ability activated). Only after the player finishes activating the crew ability (by tapping creatures he or she controls with at least enough total power) can other players do so, and even if the creatures tapped this way leave the battlefield, that doesn't mean the crew ability will fail to resolve for that reason (the crew ability doesn't target any creatures [C.R. 702.121a, 115.1c], so C.R. 608.2b doesn't apply).

EDIT (Dec. 22): Added rule citation.
EDIT (Jan. 5, Jan. 21): Clarification.
EDIT (Apr. 8): Minor edit.
EDIT (Apr. 12): Correctness edit and clarification.
EDIT (Jun. 14, 2018): Edited to conform to rule changes with Dominaria.
EDIT (Jul. 14, 2019): Some rules were renumbered with Core Set 2020.
EDIT (Sep. 3, 2019): Edited.

Quote from ReANiMaToR1 »

It seems like he can do that based upon what Kahedron stated above?

"Note unlike in chess there is no obligation to continue with an action once you have started it".

With that being said, where would the line be drawn between taking an action and making it an official move?

Sorry, I misunderstood your question in comment 1 (I misread "after paying a life..." rather than "before paying a life..."). In general, if a player has done an illegal action (for example, proposing an illegal shortcut or choosing an illegal target for a spell while casting it), the action is reversed (C.R. 725.1). In general, however, if the actions are not illegal, they are not reversed and the player must continue with the actions. If the player, though, is merely revealing the Force of Will card from his or her hand without putting it on the stack, that's not considered proposing to cast the spell (within the meaning of C.R. 601.2). (However, I am aware of an official ruling in which a player can say "not final" while declaring attackers to indicate that he or she is still deciding which creatures to attack with; this doesn't mean, however, that the player can go back to the beginning of combat step and get priority before redeclaring attackers.)

In a sanctioned tournament, a player is "not usually allowed to take back an action that has been communicated to their opponent, either verbally or physically" (M.T.R. 4.8). An exception is if a judge decides with certainty that a player "has not gained any information since taking [an unintended] action" and decides to "allow that player to change their mind" (M.T.R. 4.8).

EDIT (May 2, 2018): One rule was renumbered with Dominaria.
EDIT (Sep. 25, 2018): Correctness edit.
EDIT (Oct. 1, 2018): Edited to conform to a new M.T.R. section added with Guilds of Ravnica.
EDIT (Oct. 2, 2018; Oct. 3, 2018): Edited.
EDIT (Dec. 22, 2021): One rule was renumbered in the meantime.

Quote from ReANiMaToR1 »

When casting Force Of Will, does it make a difference in the order it's casted? For example:

1) Putting on the stack, exiling a blue card, paying 1 life.
2) Exiling a blue card, paying 1 life, putting on the stack.

And what happens when an opponent makes an illegal move like this, refusing to put the force in their graveyard, exile a blue card, and lose a life?

In sanctioned tournaments above all, it generally doesn't matter what order a player takes to cast a spell as long as the end result would have been legal if done in the correct order. Indeed, even though—

• while paying for Force of Will you can pay 1 life before you exile a blue card, or vice versa (C.R. 601.2h), and
• strictly speaking, putting a spell card on the stack must be done before paying its costs (C.R. 601.2, 601.2a, 601.2h),

the Force of Will spell would still be cast in any other order since all its costs were paid, at least where nothing in the game cares about the order (C.R. 601.2i).

Example 2 would be considered "out-of-order sequencing" under the Magic: The Gathering Tournament Rules (M.T.R. 4.3), and is unproblematic here. However, in general, once a legally cast spell resolves, it must be put into the graveyard and not back to its owner's hand (C.R. 608.2m).

EDIT (Jul. 22, 2021): Edited to conform to rule update with Adventures in the Forgotten Realms, and because one rule was renumbered in the meantime.
EDIT (Dec. 22, 2021): Edited to conform to rule update with Innistrad: Midnight Hunt.

If a Vehicle becomes a copy of a permanent without power or toughness (such as a noncreature, non-Vehicle permanent), that doesn't prevent the crew ability from making it a creature (C.R. 113.7a), but even when it does, the permanent still won't have a value for power and toughness; thus its power and toughness are undefined and so are 0/0 (C.R. 107.2; see also C.R. 208.5). (Note that C.R. 301.7b, in which a Vehicle will "immediately ha[ve] its printed power and toughness" when it becomes a creature applies only if the permanent in question is a Vehicle.)

EDIT (Jan. 12): Corrected first clause to clarify.
EDIT (Feb. 9, 2022): Edited, including because one rule was renumbered in the meantime.

According to an official ruling, which applies above all (if not only) to sanctioned tournaments, if a player taps Cavern of Souls for mana while casting a creature spell of the chosen type, it is assumed that he or she is activating its second mana ability by default, so Lord of Atlantis can't be countered. (Note that this differs from other situations in which a player could be activating one of multiple mana abilities of a single permanent if he or she taps it for mana while casting a particular spell [an example is Eldrazi Temple]: normally, a player must declare which mana ability he or she is activating in case of ambiguity [C.R. 602.2a].)

Paying Force of Will's alternative cost indicates an attempt to cast Force of Will; it can still target Lord of Atlantis even though it can't be countered (Force of Will requires only a "target spell" [C.R. 115.1a]), so the action is not illegal and can't be reversed (C.R. 725.1), and the Force of Will card remains on the stack. In general, after paying a spell's cost legally, the spell is considered cast (C.R. 601.2i). On the other hand, keeping the Force of Will card in hand after paying Force of Will's alternative cost (and casting it as a result), rather than leaving it on the stack, would be an illegal action.

EDIT (May 2, 2018): One rule was renumbered with Dominaria.
EDIT (Dec. 22, 2021): Some rules were renumbered in the meantime.

Even though Haunted Cloak has become a creature, you can still activate its equip ability targeting it (the ability requires only a "target creature you control" [C.R. 702.6a]); however, it won't be attached to itself when that ability resolves (C.R. 301.5c, 701.3b).

The difference here is that tapping the creature is part of the effect of the ability, and not a cost. If the creature can't be tapped due to Ojutai's ability, that instruction is simply ignored (C.R. 101.3) (compare with costs, which can't be paid unless the player has the resources to do so [C.R. 117.3]); if the ability had relied on the creature being untapped before you tapped it, the effect would have made tapping the creature a cost by saying, for example, "If you do, that creature doesn't untap..." (C.R. 117.12).

Assuming that a "tap ability" is an ability that requires tapping a permanent as a cost to activate it (for instance, "T: ..."), it is correct that such an ability can't be activated if the permanent in question is already tapped (C.R. 701.20a, 117.3).

EDIT (Jan. 14): Added rule citation.
EDIT (Jan. 31, 2019): One rule was renumbered with Dominaria.

axman, Muspellsheimr:

See my edit to comment 2.

1. Correct. Every creature will become a copy of Blightsteel Colossus, and the attacking and blocking creatures will have infect and assign 11 combat damage (provided nothing else happens in between). This is because after Mirrorweave resolves, attacking and blocking creatures will assign and deal combat damage based on what they will be when they do so (C.R. 613.1, especially C.R. 613.1a), rather than what they originally were.
2. This is correct, provided the Thopter is an artifact and Hellkite Tyrant's ability is still on the stack after it already dealt its combat damage to a player. (Note that Thopter is a creature type, not an artifact type [C.R. 203.5g, 203.5m]; therefore, not every Thopter is necessarily an artifact.) Every creature will become a copy of the 1/1 Thopter and will only have the abilities of that Thopter, not Hellkite Tyrant's abilities, but this doesn't affect the ability still on the stack (C.R. 112.7a), and when Hellkite Tyrant's ability resolves, you will gain control of all artifacts that player controls, including artifacts that resulted from Mirrorweave's resolution. (Note, however, that you don't have creatures assign combat damage, then cast spells before the damage is dealt [C.R. 510.2].)

EDIT: Edited because I was originally mistaken and/or I misunderstood the question.
EDIT (Dec. 16): Further corrections.
EDIT (Apr. 26, 2019): Correctness edit.

Fumigate doesn't use the word "target [something]" (or contain any keywords that do): according to C.R. 115.10a, "just because an object or player is being affected by a spell or ability doesn't make that object or player a target of that spell or ability".

On the other hand, Fumigate won't destroy creatures with indestructible (C.R. 702.12b); since destroying such creatures is impossible, the effect simply doesn't apply to them (C.R. 609.3, 101.3). (This doesn't prevent Fumigate from being cast, though.)

If a player controls two planeswalkers that share a planeswalker type (for example, Liliana in the case of the two planeswalkers you cite), even if their names differ, one of them will go to the graveyard as a state-based action (C.R. 704.5j). (This rule is distinct from the legend rule, which isn't invoked if a player controls two permanents that represent the same character, but have different names [C.R. 704.5k]).

EDIT (Feb. 14): Clarification.
EDIT (May 12): Clarification; added rule citation.
EDIT (Sep. 28): Since the planeswalker uniqueness rule will be eliminated in Ixalan, edit post accordingly.
EDIT (Mar. 6, 2021): Edited, including because one rule was renumbered in the meantime.

The word "all" on Fumigate doesn't indicate any targets. A spell has a target only if it identifies them with the form "target [something]", or any keywords it uses do (C.R. 115.10a).

EDIT (Feb. 6, 2019): Correctness edit.
EDIT (Mar. 6, 2021): One rule was renumbered in the meantime.

You would win. After combat damage is dealt, Wall of Souls's ability will have triggered and players get priority (C.R. 510.3), but first state-based actions have to be checked (C.R. 116.5). In one of those state-based actions, every player with 0 or less life will lose the game (C.R. 704.5a); this will happen even before triggered abilities (such as Wall of Souls's ability) can even go on the stack (C.R. 116.5; see also C.R. 510.3a), let alone get to resolve.