MTG Salvation

Yes. If you cast Mythos of Snapdax by paying WUBRG rather than its mana cost, then for the purposes of that spell, BR will have been spent to cast that spell, even though its mana cost wasn't paid this way.

In general, for the purposes of things that care whether certain mana "was spent to cast" a given spell, what is relevant is what mana was spent to pay that's spell's total cost, not just the mana cost or an alternative or additional cost of that spell (review C.R. 601.2f, 601.2h). (However, if the spell is copied, the copy will not have been cast, even if the original was [C.R. 706.10], so that the condition "If [certain mana] was spent to cast this spell" will be false for the copy.)

No, this can't happen.

When a player chooses a value for X as they cast, say, Genesis Hydra, that player can't choose infinity, but rather a positive integer or 0 (C.R. 107.1b, 601.2b).

Neither can a player have an infinite amount of mana; if a player has a way to add an arbitrary amount of mana, that player can only carry out that process a finite number of times (say, one million) (see C.R. 721.2a and, in sanctioned tournaments, M.T.R. 4.4). (This of course ignores "silver-bordered" cards such as Mox Lotus, which were designed for fun rather than necessarily conforming to the rules [see also C.R. 100.7].)

Finally, a creature's power or toughness can't be infinite, but rather can be an integer only, including zero (C.R. 107.1, especially C.R. 107.1b).

Remember that in general, "[t]he only numbers the Magic game uses are integers" (C.R. 107.1).

It depends. If the spell uses the word "target" more than once to indicate separate targets, the same object can be chosen more than once if it meets the spell's targeting criteria each time (e.g., Seeds of Strength, Hidden Strings). However, if the spell uses the word "target" only once to indicate one or more targets, the same object can't be chosen more than once (e.g., Counterspell). Note also that "choos[ing] new targets" for a spell doesn't let you change the number of targets the spell has (review C.R. 115.7d; for this case in particular, see also C.R. 706.10c).

See also C.R. 601.2c and 114.1, as well as this thread.

Note that in the case of Counterspell, if the original and its copy target the same spell and the copy counters that spell, the countered spell will be an illegal target for any other spell or ability that targeted the countered spell, including the original Counterspell (C.R. 608.2b, 701.5a). See also this thread and this thread.

You are correct.

Since you controlled Oath of Druids at the time its ability triggered, namely as the upkeep began, the hexproof you have doesn't apply to that ability, since it isn't an "abilit[y] your opponents control" (C.R. 109.5, 702.11c). Thus, the player whose upkeep the ability refers to has to target a "player who controls more creatures than they do and is their opponent", as normal (note that targeting isn't optional [C.R. 601.2c]). Compare hexproof with shroud, which applies to any "spel[l] or abilit[y]" no matter who controls it (compare C.R. 702.11c with C.R. 702.18a).

The rules for the Commander variant changed with Core Set 2021 in a way that materially affects these answers.

The answers are now as follows, assuming you're playing the Commander variant under C.R. 903:

1. If your commander is exiled, it will go to exile (rather than "redirect" to the command zone), then a state-based action will give you the choice of moving it to the command zone (C.R. 903.9a). If you move it this way, however, Grasp of Fate won't return your commander to the battlefield (even if the commander returns to exile before it would do so), since your commander has left exile (C.R. 400.7, 610.3). Your commander will return this way only if it hasn't left exile in the meantime (C.R. 610.3). This answer applies to anything that says "exile ... until ...", such as found in Grasp of Fate.
2. You can't choose to move your commander to the command zone instead of to exile when Momentary Blink exiles and returns your commander, as state-based actions don't happen while a spell or ability is resolving (C.R. 704.4, 117.2a, 117.5, 903.9a). This answer applies to anything that says "exile ..., then return ...", such as found in Momentary Blink.
3. Yes (assuming Progenitus is your commander), since Progenitus would otherwise go to the graveyard (C.R. 616.1). (Note, however, that if Progenitus is your commander, you can no longer choose to move Progenitus to the command zone instead of into exile or your graveyard.)
4. In this case, if you choose to put Bruna into the command zone instead of your hand or library, the Gisela card won't go as well, but rather is "put into the appropriate zone" (C.R. 903.9b-c). The word "may" is used in the place you mention because the commander's owner may move it to the command zone instead of to one of the zones dictated by two or more replacement effects other than that under C.R. 903.9b, if there are any such effects. In any case, the second sentence of C.R. 712.4d is merely referring to another rule, so that here, C.R. 903.9c takes precedence. However, if Brisela, Voice of Nightmares is your commander on the battlefield and moves to exile or the graveyard, all of its components go there (including Gisela), then a state-based action will give you the choice of moving Bruna to the command zone (C.R. 903.9a).

For completeness, I cover the following two cases:

1. The case of Astral Slide and other effects that exile a permanent and set up a delayed triggered ability to return that card to the battlefield at a later time, such as "at the beginning of the next end step". In this case, if your commander is exiled this way, it will go to exile, then a state-based action will give you the choice of moving it to the command zone (C.R. 903.9a). If you move it this way, however, the delayed triggered ability won't return your commander to the battlefield (even if it returns to exile before it would do so), since your commander has left exile (C.R. 400.7). Your commander will return this way only if it hasn't left exile in the meantime.
2. The case of Oblivion Ring and other permanents with linked abilities, one of which exiles a permanent and the other returns "the exiled card" to the battlefield (C.R. 607.1). In this case, if your commander is exiled this way, it will go to exile, then a state-based action will give you the choice of moving it to the command zone (C.R. 903.9a). If you move it this way, however, your commander will no longer count as an "exiled card" this way (C.R. 607.2a): the second ability can return only "the exiled card" to the battlefield, which means a card still in exile that was put there due to the first ability (C.R. 607.2a). Your commander will return this way only if it hasn't left exile in the meantime.

Yes, a phased-out token, even one named Marit Lage, will phase in just fine, just like any other phased-out permanent (C.R. 111.6; note that C.R. 702.25a is not limited to nontoken permanents).

The rules for the Commander variant changed with Core Set 2021 in a way that materially affects this answer.

The answer to comment 1 is now: No, this won't work, even if you're playing the Commander variant, which has C.R. 903.9, and Mairsil is your commander.

Now, if Mairsil is your commander and you exile Mairsil with the ability it gains from Shifty Doppelganger, a state-based action will then give you the option to move Mairsil from exile to the command zone (C.R. 903.9a). If Mairsil moves to the command zone this way, however, the ability won't bring Mairsil back to the battlefield, since it has left exile (C.R. 400.7, especially C.R. 400.7h). Mairsil will return this way only if it hasn't left exile in the meantime.

The rules for the Commander variant changed with Core Set 2021 in a way that materially affects this answer.

The answer is now: In general, only if the commander's owner chooses to leave the commander in their graveyard and it doesn't leave that graveyard before Rescue from the Underworld returns it to the battlefield.

Now, in general, if a commander is sacrificed with Rescue from the Underworld, it will go to the graveyard as normal (C.R. 701.16a). And a state-based action gives its owner the option to move their commander from the graveyard to the command zone (C.R. 903.9a). If the commander moves to the command zone this way, however, Rescue from the Underworld won't bring that commander back to the battlefield, since it has left the graveyard (C.R. 400.7, especially C.R. 400.7h). The commander will return this way only if it hasn't left the graveyard in the meantime.

Only once. If Doom Blade is a "car[d] exiled with Nightveil Specter" and you then cast Doom Blade from exile, it will no longer count as a "car[d] exiled with Nightveil Specter" since it's no longer in exile (C.R. 607.2a). (Note that in general, a spell goes to its owner's graveyard when it resolves, even if it was cast from exile [C.R. 608.2k].) In general, you then won't be able to cast Doom Blade again with Nightveil Specter even if Doom Blade returns to exile (unless it returns to exile again due to Nightveil Specter's first ability). See also this thread.

To be clear:

In general, a creature can block no more than one creature, regardless of power and toughness (C.R. 509.1a). But if an effect (such as Brave the Sands) lets a creature block more than one creature, it can do so regardless of power and toughness. This means, for example, that Brave the Sands lets a "creature you control" block two other creatures regardless of their power and toughness (e.g., a 1/5 "creature you control" can block a 6/2 creature and another creature just fine this way).

Yes. Every Aura spell requires a target (C.R. 115.1b), so that if you control Willbreaker or Cowardice and target a "creature an opponent controls" or a "creature", respectively, with Sluggishness, Willbreaker's or Cowardice's ability will trigger (compare with Silverfur Partisan).

Likewise, for the purposes of those two abilities, even a mutating creature spell such as Archipelagore is a "spell or ability" (C.R. 115.1e).

EDIT: Correctness edit after comment 3 was posted.

Your team can't attack with Vantress Gargoyle in this scenario.

In Two-Headed Giant, Vantress Gargoyle can attack only if the player (or controller of the planeswalker) it's attacking (and only that player) has seven or more cards in their graveyard (so not, for example, if one player in the team has only three and the other has only four cards in their graveyard) (C.R. 805.10e, 810.7).

This is because, "[f]or each attacking creature, the attacking team announces which defending player or planeswalker that creature is attacking", and it's only that player (or the controller of that planeswalker) that the phrase "defending player" on Vantress Gargoyle refers to (C.R. 805.10b, 805.10e, 810.7).

Yes. If Player A casts a Sliver spell while they control The First Sliver, that spell's cascade ability will trigger (C.R. 109.5). It will get to resolve even if The First Sliver is removed from the battlefield (and the Sliver spell is no longer given cascade) in the meantime (C.R. 603.3, 611.3b, 113.6). However, before it resolves, Player B (and every other player) will have priority to cast instant spells and activate abilities (including Murder or another spell that would remove The First Sliver from the battlefield) (C.R. 117.4, 117.1a-b). And if The First Sliver is removed from the battlefield before cascade resolves, its last ability won't give cascade to any spells anymore, including a Sliver spell cast due to cascade (C.R. 611.3b, 113.6).

Quote from Craterallus »

So let's say I'm down to one card in hand and it has madness, I tap anje falkenrath, pay the madness cost to cast the spell I'm discarding and draw a card - if that spell is not a madness card, but is instead a cycling card like canyon slough - presuming I have the mana - can I cycle it before I have to discard it to oppression due to it being a mana ability and not going on stack?

Assuming Canyon Slough is the card you just drew, yes. Oppression's ability, like any other triggered ability, has no effect unless and until it resolves. And the ability doesn't do anything immediately after you discard a card, and you can activate an ability (including cycling) in response to Oppression's ability as you can to nearly any other triggered ability on the stack.

What if the card I draw is a second madness card and anje falkenrath untaps - can I tap her again on stack before the oppression trigger forces me to discard, and discard it with Anje to draw another card first?

Yes.

What if I draw a non-cycling non-madness instant like terror? Can I cast it at instant speed in response to the oppression trigger?

Yes.

If I have no cards in hand when the oppression triggers finally resolve - I don't have to anything, right?

Correct. If you can't discard a card, there is no further consequence (C.R. 101.3).

Quote from Craterallus »

Great, final question re; cowardice

What about targeting with a spell like Rhystic Deluge? Even if they pay the one to avoid the effect they are still being targeted and thus get bounced, no?

Correct. Rhystic Deluge's ability targets a creature, so Cowardice's ability will trigger for that creature. If a creature "becomes the target of a spell or ability", Cowardice's ability will trigger, no matter what that spell or ability would do when it resolves and even if the spell or ability says "unless [a player] pays...".