MTG Salvation

In this case, Anger of the Gods would deal 3 damage to Auriok Champion, Daunting Defender, and Rosheen Meanderer. (I assume Player A chooses Anger of the Gods as the source for Harm's Way.)

For Auriok Champion, there are three replacement and/or prevention effects involved: protection from red (C.R. 702.16e), Daunting Defender, and Harm's Way. Player A, as the controller of Auriok Champion, chooses which one applies (C.R. 616.1, 616.1d). If Daunting Defender is chosen, 1 of the damage is prevented; if protection from red is chosen, all of the damage is prevented; and if Harm's Way is chosen, 2 of the damage is dealt instead to Rosheen Meanderer (provided there is still damage Harm's Way can prevent this way). The remaining damage is handled (as far as applicable) by the remaining replacement and/or prevention effects, and whoever controls the creature that would now be dealt damage chooses one of them to apply, and so on (C.R. 616.1e, 616.1).

For Daunting Defender, there are two replacement and/or prevention effects involved: Daunting Defender and Harm's Way. Player A, as the controller of Daunting Defender, chooses which one applies, in the same way (C.R. 616.1).

For Rosheen Meanderer, no relevant replacement or prevention effects apply, so Rosheen Meanderer will be dealt 3 damage.

This answer doesn't change if Anger of the Gods is cast by a different player or on a different turn. Whether a prevention effect (such as Anoint) or a replacement effect (such as Harm's Way) is involved is irrelevant.

EDIT (Mar. 29): Correctness edit.

An official ruling published in October 2017's Magic Judge Monthly confirms that if an effect has the form "... may search ... then shuffle ..." (such as found in Ghost Quarter or Path to Exile), a player can't choose to shuffle the library due to that effect if he or she can't search it (C.R. 608.2d).

An official ruling published in October's Magic Judge Monthly confirms the first sentence of my comment 2 and applies to all effects of the form "... may search ... then shuffle ..." (but using Ghost Quarter and Leonin Arbiter instead of Infectious Bloodlust and Shadow of Doubt, respectively).

With the understanding that no Magic card (other than "silver-bordered" cards) has such an effect as that of either of Graveyard Busybody's abilities:

The word "also" in Graveyard Busybody's first ability suggests that each graveyard is treated as "your graveyar[d]" in addition to being treated as its owner's. Thus, every other player still has a graveyard despite that ability. In the case of Exhume, though, there is a difficulty if you and another player want to return the same creature card to the battlefield; in which case C.R. 101.4 (the APNAP order rule) can be applied.

EDIT: See also comment 3 and the second note below this one. Note, however, that because no Magic card (other than "silver-bordered" cards) has such an effect as that of Graveyard Busybody's first ability, the comprehensive rules do not regulate, and therefore cannot answer, whether a graveyard that is "also" a particular player's graveyard is still the graveyard of its original owner.

EDIT (Jan. 16): Correctness edit in view of changes to the Magic Tournament Rules with Rivals of Ixalan.

EDIT (Jan. 2, 2019): Note that the comprehensive rules do not regulate, and therefore cannot answer, whether a graveyard that is "also" a particular player's graveyard is still the graveyard of its original owner. In general, in a game allowing "silver-bordered" cards such as those in Unglued, Unhinged, and Unstable, the players in the game can agree on modifications to the comprehensive rules ("house rules") to accommodate situations, such as this one, that the comprehensive rules neither regulate nor answer and that are unique to such cards (see also C.R. 100.7). Although Mark Rosewater issues "rulings" on how certain game situations unique to such cards play out, such advice is no more or less valid than the "house rules" agreed to by the players (that is, such players can agree whether to adopt such "rulings" or not).

EDIT (Jan. 26, 2019): Struck out more text.

In Spell Shrivel, "Counter target spell unless its controller pays 4" means "Target spell's controller may pay 4. If that player doesn't, counter that spell" (C.R. 117.12a).

The sentence "If that spell is countered this way, exile it instead of putting it into its owner's graveyard" expresses a self-replacement effect; it changes what countering a spell with Spell Shrivel does (C.R. 614.15; see C.R. 701.5 for what countering a spell normally does; another example is Remand).

Quote from fahrenheights »

I found on Maro's blog here a similar question about text boxes and various printings having different effects:

Tainted Monkey naming the word "add" would affect older basic lands that have the word "Add" in the text box.

Which is hilarious because that means the Masterpiece editions of Mana Vault and Sol Ring are worse than revised editions for a Baron Von Count deck.

With respect to that "ruling", compare—

• C.R. 305.6, which grants a "land with a basic land type" the corresponding "intrinsic ability" "even if the text box doesn't actually contain that text or the object has no text box", with
• C.R. 306.5, which treats a planeswalker's text box as if it included a certain ability.

Quote from DementedKirby »

Exactly, that's my reasoning. If the object is already on the battlefield and copies a contraption, it would become the contraption but it really wouldn't do anything because it doesn't trigger. My Mirage Mirror won't go to the graveyard because it's already in play.

That statement is reasonable. Since I don't expect the comprehensive rules to include any rules, let alone rigorous ones, for how assembling Contraptions and the Contraption Deck work, that leaves only that Unstable game mechanics article and any "house rules" the players may impose to fill any rigor gaps in this matter.

EDIT: Struck out a sentence after comment 12 was posted.
EDIT (Jan. 3, 2019): Struck out second sentence.

Quote from user_938036 »

While this is true for all normal cases, Uncards actually use the printed card when referencing aspects of that card.

That is generally the case only if all the players in the game agree to modify C.R. 108.1 (that is, impose a "house rule" on the matter). But see R&D's Secret Lair, an Unhinged card that directly contradicts C.R. 108.1 when it says to "(i)gnore all errata" (C.R. 101.1).

Quote from DementedKirby »

But if I copy it, it doesn't get cranked because it's not on a sprocket, right?

After reading the article further, I find that in fact says that if "a Contraption ... find[s] its way onto the battlefield without being assembled[,] the card either goes to the scrapyard if it's an actual Contraption card or it goes to the graveyard if it's not." The article, however, doesn't state whether that is a state-based action. Moreover, the article speaks of assigning a Contraption to a sprocket only if it's assembled, and not in any other circumstance.

A permanent can become a copy of a Contraption as it can become one of any other artifact (see also C.R. 205.3g). However, according to the mechanics article for Unstable, if "a Contraption ... find[s] its way onto the battlefield without being assembled[,] the card either goes to the scrapyard if it's an actual Contraption card or it goes to the graveyard if it's not".

EDIT: Correction after comment 5 was posted.

Quote from darrenhabib »

Thanks. I have another question. Some older cards like Mana Vault have the text 3, but in newer additions would be seen as "three" or CCC.
Is there an official ruling for what wording is exactly on a card? Like are cards errata to read as the newest additions?

Use the text found in the Oracle card reference to determine a card's wording (C.R. 108.1). For example, the Oracle text of Mana Vault's last ability is "T: Add CCC to your mana pool." at the time of this writing.

When the Malakir Bloodwitch that just resolved enters the battlefield, both its ability and that of Flameshadow Conjuring will trigger simultaneously and will go on the stack at the same time (C.R. 603.10, 116.3b, 116.5, 603.3b, 603.6a); however, since you control both abilities, you can order them on the stack as you want (C.R. 603.3b) (they each get to resolve, though, only if all players pass in a row [C.R. 116.4]). Note that Flameshadow Conjuring's ability won't trigger when the token that's a copy of Malakir Bloodwitch enters the battlefield, since a token is not a "nontoken" creature.

Panoptic Mirror lets you cast a copy of the card exiled with it only during your upkeep when its triggered ability resolves (C.R. 603.2, 608.2c, 608.2f), and not at any other time, including during other steps or phases of your turn or during turns other than yours (compare Panoptic Mirror with Isochron Scepter, which uses an activated ability you can activate any time you have priority, not just during your upkeep [C.R. 116.1b]).

Therefore, if the spell has you add mana, generally that mana will be added during your upkeep and any unused mana will be lost as that upkeep ends (C.R. 500.4). (Whether exiling a particular card with Panoptic Mirror is "useless" under particular circumstances is a strategy question, not a rule question, so is out of scope for this forum.)

EDIT (Dec. 24): Add rule citation.
EDIT (Aug. 3; Mar. 18, 2019): Correctness edit in view of Dominaria update.

Flash puts a creature card onto the battlefield (if you choose so), so any abilities that trigger due to that action, including the second ability of Riku of Two Reflections, will trigger (C.R. 603.2). Whether you choose to pay its mana cost reduced by up to 2 is irrelevant. This is because triggered abilities can trigger even in the middle of a spell or ability resolving (C.R. 603.2a; see also C.R. 704.4).

Note that in the scenario given, the first ability of Riku of Two Reflections will trigger when you cast Flash; it will go on the stack above Flash (C.R. 405.2) and get to resolve before it (C.R. 116.4). For purposes of this scenario, though, I assume you choose not to pay UR when that ability resolves.

EDIT (Mar. 2): Correctness edit.

It does depend on the order in which Conspiracy and Arcane Adaptation entered the battlefield, namely, their timestamp order (neither effect depends on the other within the meaning of C.R. 613.7a, since among other things, they both affect the same things, namely "[c]reatures you control", "creature spells you control", and "creature cards you own that aren't on the battlefield", and neither changes what the other applies to) (C.R. 613.1d, 613.6, 613.6a, 613.6c). Thus in your example, if Conspiracy entered before Arcane Adaptation, creatures you control (among other things) would have only the Scarecrow and Goblin creature types (C.R. 205.1a-b). The other way around, creatures you control (among other things) would have only the Scarecrow creature types (C.R. 205.1a-b).