MTG Salvation

Yes. Because you controlled Whip of Erebos as you sacrificed Bloodfire Colossus, Bloodfire Colossus had lifelink at the last moment it was on the battlefield, so it will deal damage and gain you that much life (C.R. 120.3f, 113.7a). This is true even if Whip of Erebos leaves the battlefield after you activate Bloodfire Colossus's ability but before it resolves.

EDIT (Feb. 4, 2021): Some rules were renumbered in the meantime.

That is correct. In general, "you may..." on a triggered ability is a choice made only as the ability resolves (C.R. 603.5), so without any other player knowing whether you will choose that option before it resolves. However, you must choose legal targets as you put the ability on the stack if the ability requires them, even if you decide not to exercise the "you may..." choice (C.R. 603.3d, 601.2c-d). If you can't choose the required number of legal targets, the ability is removed from the stack and won't resolve (C.R. 603.3d).

Yes. The controller of Moonsilver Spear when the equipped creature attacks puts the Angel token onto the battlefield, no matter who controls the equipped creature when it attacks.

DRay273:

But see, for example, Solemn Simulacrum and Squadron Hawk, which do use "You may search ..., then shuffle ...", and not, say, "Its controller may search ..., then shuffle ...".

DRay563:

I don't think that applies to Ghost Quarter or Path to Exile, which are both of the form "You may search ..., then shuffle ..." rather than "You may search ... If you do, shuffle ...", and the latter form is clearly covered in C.R. 117.12 (an example is found in Trinket Mage). More generally, if an effect is of the form, "[A player] may A, then B" but A is impossible, can the player still choose to do B?

EDIT (Dec. 9, 2017): See comment 10.

With Abundance, the card draw is replaced with an event that doesn't involve card draws, so as a result, no cards are "drawn". But as long as you choose to draw cards with Sylvan Library, you must still "choose two cards in your hand drawn this turn", which in this case are cards in your hand drawn this turn, where the draws weren't replaced with something else. This is true even if one or both of the card draws from Sylvan Library are replaced with something else (C.R. 117.11, 117.12). (C.R. 120.6c doesn't apply here because Abundance doesn't replace drawing with drawing and another event, and Sylvan Library doesn't do something with a particular card that was drawn with its ability.)

EDIT (Dec. 23): Added rule citation.
EDIT (Apr. 12, 2018): Clarification.

Abilities of the form "As long as your devotion ... is less ..., [this object] isn't a creature", as possessed by Keranos, for example, work only while the objects that have them are on the battlefield (C.R. 112.6), so not while they're anywhere else, including on the stack. Therefore, Keranos counts as a creature spell regardless of your devotion to red and blue, and Keranos may or may not enter the battlefield as a creature depending on your devotion to red and blue (taking into account Keranos and any other newcomers on the battlefield) (C.R. 603.6a-b).

EDIT (Apr. 10, 2017; Sep. 11, 2018): Correctness edit.

Yes. When Sin Prodder's ability resolves, you still do everything possible under that ability, and Sin Prodder can still deal damage even though it has left the battlefield. In general, a triggered ability of a permanent, once triggered, is unaffected by that permanent leaving the battlefield (C.R. 112.7a).

EDIT (Dec. 9): Clarification.

Whether a spell was "cast" is not a copiable value (C.R. 706.2). Rather, the card exiled with Ertai's Meddling is "pu[t] ... onto the stack" without following the rules for casting a spell (found in C.R. 601.2). Thus, for the purposes of Containment Priest, the spell "wasn't cast". (Copies of instant and sorcery spells, such as with Twincast, aren't "cast", either [C.R. 706.10].)

EDIT (Sep. 23, 2016): Made clarification.
EDIT (Nov. 22, 2017): Minor edit; added rule citation.

When a nontoken creature enters, whoever controls the creature when Dual Nature's first ability resolves will create a token that's a copy of whatever that creature is (ques. 1) or whatever it's copying (ques. 3) (C.R. 706.2).

If that creature leaves the battlefield as a creature (ques. 2 and 4), the second ability will trigger and, when it resolves, exile all tokens with the same name as whatever the creature was at the last moment it was on the battlefield (C.R. 112.7a). Then when the first ability resolves, the last controller of that creature will create a token that's a copy of whatever the creature was when it left.

EDIT (Dec. 9, 2017): Edited due to change in terminology.

Creature A will enter as a copy of that creature and acquire its "copiable values" (C.R. 706.2), and how long creature A will keep those values is independent of how long the effect on the other creature lasts. For instance, if creature A is Clone, the effect lasts as long as it's on the battlefield. If creature A is Vesuvan Shapeshifter, it lasts until Vesuvan Shapeshifter is turned face down.

If you control one Hardened Scales, the number of +1/+1 counters you put on a creature is increased by one; if you control two Hardened Scales, you put that many +1/+1 counters plus two; if three, that many plus three, and so on. This is so because Hardened Scales's effect replaces something with more of it, so that each Hardened Scales effect can apply to the replaced event (C.R. 616.1e). (Note that the counters are not doubled, tripled, etc. For example, with Karlov of the Ghost Council's first ability, the number of +1/+1 counters you put on that creature is only increased by the number of Hardened Scales you control, so that number is three -- not four -- if you control one Hardened Scales, for instance.)

Note that Chasm Skulker's abilities resolve separately, so you put a +1/+1 counter each time, and not all of them at once; as a result, you put an increased number of counters each time with Hardened Scales. For example, if you draw two cards and control one Hardened Scales, you put four +1/+1 counters total on the creature (assuming all the abilities from Chasm Skulker resolve); if you control two, six total; and so on.

EDIT (Jun. 30, 2018): Minor change in terminology.

After Krosan Grip resolves, state based actions are checked before any player gets priority (so even before players can cast more spells or activate more abilities) (C.R. 116.5). If Phyrexian Unlife has left the battlefield (due to Krosan Grip), this can cause Phyrexian Unlife's controller to lose the game for having 0 or less life, since Phyrexian Unlife is no longer on the battlefield to stop it (C.R. 112.6, 704.5a).

In general, while a player casts a spell or activates an ability, no other spells or abilities can be cast or activated or even resolve (including those that would keep the player from paying the spell or ability's costs, such as Abrupt Decay or Pongify to destroy the creature that would be sacrificed for Prossh's ability), because players don't have priority at this time (C.R. 601.2a-i and 602.2a-b have no priority window until the spell is cast or ability activated). The exception is that the player can activate and resolve mana abilities if the cost includes a mana payment (C.R. 601.2g).

Note that you can sacrifice several creatures using Prossh's ability before passing priority, because a player who had priority to activate an ability gets priority after doing so (C.R. 601.2i).

Any abilities that trigger from a creature dying due to the sacrifices, including those from Blood Artist, Vicious Shadows, etc., will trigger and go on the stack, and those triggered abilities will stay on the stack no matter what happens to Blood Artist, etc. (C.R. 112.7a). (Such abilities are part of a category of abilities called "leaves-the-battlefield abilities"; as a result, they can trigger even if their source dies at the same time [C.R. 603.6c, 603.10, 603.10a].)

Because you sacrifice one creature, and not several, each time you activate Prossh's ability, and triggered abilities (including those from Blood Artist, etc.) go on the stack before you get priority again (C.R. 116.5), the triggered abilities on the stack will be ordered such that the ability triggered by the most recently sacrificed creature is placed on top; this can matter, for instance, in the case of Stalking Vengeance's triggered ability.

As a result, it matters what order you sacrifice the creatures. If you sacrifice Blood Artist before sacrificing the other creatures, it won't trigger for those other creatures, since it isn't on the battlefield anymore (C.R. 113.6). (Note that you don't "sacrifice all of them", since Prossh can't be sacrificed itself with its ability.)

EDIT (Dec. 7): Some rules were moved in Commander 2016.
EDIT (Nov. 3, 2019): One rule was renumbered with Core Set 2020.

Shaman's Trance refers to "play[ing] lands and cast[ing] spells from other players' graveyards"; it doesn't let you target cards from those graveyards (as with Mizzix's Mastery) or grant abilities to those cards (as with Past in Flames) as though those cards were in your graveyard.

EDIT (Sep. 19, 2020): Correctness edit.
EDIT (May 9, 2021): Edited to conform to recent Oracle text changes.