1. Do I need to declare for Prized Amalgam the first Prized Amalgam trigger, when a Haunted Dead or Stitchwing generates a delayed trigger? I've heard someone say I don't have to at all but I'm skeptical, especially since it can carry from my own end step to my opponent's.
2. If I forget my second prized Amalgam trigger and untap my permanents, but before doing anything at all, before drawing a card, realize the Prized Amalgams are still in the yard, can I put them into play? I have priority on my upkeep so it seems like that would be forgivable. But then again some competitive REL rules, like pacts, are savage, so.
3. Can I "miss" triggers by trying to resolve some of my triggers before explicitly declaring that all of them are on the stack? For instance, if I say, "I tap 8 mana and cast Elder Deep-Fiend. Assuming you don't Disallow it, I exile Kozilek's Return from my graveyard to kill all your dudes. <waits for opponent to physically move dudes> Oh, Elder Deep-Fiend taps your four Forests. Oh, I sacrifice Sanctum of Ugin and go grab an Ornithopter.
I suspect it's possible that the Sanctum of Ugin trigger is ok not to say stuff about, but that the targeted trigger has to be acknowledged immediately. After all, it seems a little unfair for an opponent not to know that casting Heroic Intervention using lands that will soon be tapped down anyway soon is a good idea until after putting creatures into their graveyard and realizing that Elder Deep-Fiend has a tapdown trigger. (even though that feature of Elder Deep-Fiend seems pretty prominent, at the end of the day it's not the victim's card) Whereas, the Sanctum of Ugin trigger doesn't target and doesn't do much to affect game state before it resolves.
4. It seems like if I discard a total of four cards to return two different Haunted Deads to the battlefield, a single Prized Amalgam in my graveyard would create 2 triggers that generate 2 delayed triggers that are both put on the stack at the beginning of the next end step. Thus, a single Disallow or Nimble Obstructionist cycle would be insufficient to prevent the zombie from returning to the battlefield, since another trigger with rules text describing the same zone change goes on the stack. But a friend of mine said "it's not like that on MTGO", which is, ok, I believe him, but I don't understand the rules basis for it. What actually happens?
In sanctioned tournaments in general, Prized Amalgam's delayed triggered ability is forgotten "once the player takes an action past the point where the triggered ability would have an observable impact on the game" (M.T.R. 4.5).
Assuming this is a sanctioned game at Competitive or Professional rules enforcement level:
1. Under I.P.G. 2.1, Prized Amalgam's ability (that triggers when a creature enters the battlefield in certain circumstances) "do[es] nothing except create [a] delayed triggered abilit[y]", so that ability itself need not be acknowledged until the delayed triggered ability must be.
2. In this scenario, if you "t[ook] any game actions ... that c[ould] be taken only after" Prized Amalgam's delayed triggered ability "should have resolved" (since that ability "causes a change in the visible game state"), then a judge may assess an infraction against you, especially if they "intend to issue a Warning" or suspect the ability is intentionally forgotten (I.P.G. 2.1).
3. Elder Deep-Fiend's last ability requires "its controller to choose targets ... or other choices made when the ability is put on the stack" (including, in this case, the number of targets), so those choices must be made before you next pass priority (I.P.G. 2.1; C.R. 115.1a). Note, though, that under the Magic Tournament Rules, in general, a player passes after adding an object to the stack (M.T.R. 4.2, third and fourth listed shortcuts). Note also that in the scenario given here, three abilities have triggered at the same time: Elder Deep-Fiend's, Kozilek's Return's, and Sanctum of Ugin's last abilities. Since you control all three (C.R. 113.8), you may put them on the stack in any order (C.R. 603.3b). In certain circumstances, though, the order in which you put them on the stack may be relevant; for example, in this scenario, you declared how Elder Deep-Fiend's ability will resolve without mentioning the order of the other two abilities. This can also be problematic independently of whether Elder Deep-Fiend's ability requires choosing whether or how it targets under C.R. 603.3d and C.R. 601.2c.
Assume, however, that Elder Deep-Fiend's last ability doesn't require any player to choose whether or how it targets. Under this assumption, neither Kozilek's Return's nor Sanctum of Ugin's ability requires targets or affects the game state before resolving within the scope of I.P.G. 2.1, and nothing in this scenario cares about the order of those two abilities on the stack by the time Elder Deep-Fiend's ability resolves. (EDIT [Jul. 20]: Note, however, that under M.T.R. 4.3, "[p]layers may not try to use opponent's [sic] reactions to some portion of an out-of-order sequence" — here, declaring the order of triggered abilities only after resolving Elder Deep-Fiend's first ability — to decide what actions to take [see also C.R. 721.2a, which requires a player proposing a shortcut to "describ[e] a sequence of game choices, for all players, that may be legally taken"; the shortcut in question here, though, is "I tap 8 mana ... kill all your dudes", which doesn't include the order in which other triggered abilities that won't resolve during the shortcut exist on the stack].)
The following answer applies to both sanctioned and unsanctioned games:
4. You were right originally. Prized Amalgam's ability triggers each time a creature enters the battlefield from your graveyard (among other circumstances) while Prized Amalgam is in your graveyard (C.R. 603.2, 113.6k). Thus, to achieve the goal stated here, each ability triggered this way needs to be countered or otherwise leave the stack before it resolves and creates a delayed triggered ability (C.R. 603.7a; only if it resolves are its instructions followed under C.R. 608.2c).
EDIT (Dec. 9): Deleted second sentence in answer 2.
EDIT (Jan. 19, 2018): Changed a rule citation to conform to changes in the Magic Tournament Rules with Rivals of Ixalan.
EDIT (Jul. 6, 2018): One rule was renumbered with Dominaria.
EDIT (Jul. 14, 2018): One rule was renumbered with Core Set 2019.
EDIT (Mar. 17, 2019): Correctness edit.
EDIT (Jan. 25, 2020): Edited, including because some rules were renumbered with Core Set 2020.
2. If I forget my second prized Amalgam trigger and untap my permanents, but before doing anything at all, before drawing a card, realize the Prized Amalgams are still in the yard, can I put them into play? I have priority on my upkeep so it seems like that would be forgivable. But then again some competitive REL rules, like pacts, are savage, so.
3. Can I "miss" triggers by trying to resolve some of my triggers before explicitly declaring that all of them are on the stack? For instance, if I say, "I tap 8 mana and cast Elder Deep-Fiend. Assuming you don't Disallow it, I exile Kozilek's Return from my graveyard to kill all your dudes. <waits for opponent to physically move dudes> Oh, Elder Deep-Fiend taps your four Forests. Oh, I sacrifice Sanctum of Ugin and go grab an Ornithopter.
I suspect it's possible that the Sanctum of Ugin trigger is ok not to say stuff about, but that the targeted trigger has to be acknowledged immediately. After all, it seems a little unfair for an opponent not to know that casting Heroic Intervention using lands that will soon be tapped down anyway soon is a good idea until after putting creatures into their graveyard and realizing that Elder Deep-Fiend has a tapdown trigger. (even though that feature of Elder Deep-Fiend seems pretty prominent, at the end of the day it's not the victim's card) Whereas, the Sanctum of Ugin trigger doesn't target and doesn't do much to affect game state before it resolves.
4. It seems like if I discard a total of four cards to return two different Haunted Deads to the battlefield, a single Prized Amalgam in my graveyard would create 2 triggers that generate 2 delayed triggers that are both put on the stack at the beginning of the next end step. Thus, a single Disallow or Nimble Obstructionist cycle would be insufficient to prevent the zombie from returning to the battlefield, since another trigger with rules text describing the same zone change goes on the stack. But a friend of mine said "it's not like that on MTGO", which is, ok, I believe him, but I don't understand the rules basis for it. What actually happens?
Thanks in advance if there is any input!
Assuming this is a sanctioned game at Competitive or Professional rules enforcement level:
1. Under I.P.G. 2.1, Prized Amalgam's ability (that triggers when a creature enters the battlefield in certain circumstances) "do[es] nothing except create [a] delayed triggered abilit[y]", so that ability itself need not be acknowledged until the delayed triggered ability must be.
2. In this scenario, if you "t[ook] any game actions ... that c[ould] be taken only after" Prized Amalgam's delayed triggered ability "should have resolved" (since that ability "causes a change in the visible game state"), then a judge may assess an infraction against you, especially if they "intend to issue a Warning" or suspect the ability is intentionally forgotten (I.P.G. 2.1).
3. Elder Deep-Fiend's last ability requires "its controller to choose targets ... or other choices made when the ability is put on the stack" (including, in this case, the number of targets), so those choices must be made before you next pass priority (I.P.G. 2.1; C.R. 115.1a). Note, though, that under the Magic Tournament Rules, in general, a player passes after adding an object to the stack (M.T.R. 4.2, third and fourth listed shortcuts). Note also that in the scenario given here, three abilities have triggered at the same time: Elder Deep-Fiend's, Kozilek's Return's, and Sanctum of Ugin's last abilities. Since you control all three (C.R. 113.8), you may put them on the stack in any order (C.R. 603.3b). In certain circumstances, though, the order in which you put them on the stack may be relevant; for example, in this scenario, you declared how Elder Deep-Fiend's ability will resolve without mentioning the order of the other two abilities. This can also be problematic independently of whether Elder Deep-Fiend's ability requires choosing whether or how it targets under C.R. 603.3d and C.R. 601.2c.
Assume, however, that Elder Deep-Fiend's last ability doesn't require any player to choose whether or how it targets. Under this assumption, neither Kozilek's Return's nor Sanctum of Ugin's ability requires targets or affects the game state before resolving within the scope of I.P.G. 2.1, and nothing in this scenario cares about the order of those two abilities on the stack by the time Elder Deep-Fiend's ability resolves. (EDIT [Jul. 20]: Note, however, that under M.T.R. 4.3, "[p]layers may not try to use opponent's [sic] reactions to some portion of an out-of-order sequence" — here, declaring the order of triggered abilities only after resolving Elder Deep-Fiend's first ability — to decide what actions to take [see also C.R. 721.2a, which requires a player proposing a shortcut to "describ[e] a sequence of game choices, for all players, that may be legally taken"; the shortcut in question here, though, is "I tap 8 mana ... kill all your dudes", which doesn't include the order in which other triggered abilities that won't resolve during the shortcut exist on the stack].)
The following answer applies to both sanctioned and unsanctioned games:
4. You were right originally. Prized Amalgam's ability triggers each time a creature enters the battlefield from your graveyard (among other circumstances) while Prized Amalgam is in your graveyard (C.R. 603.2, 113.6k). Thus, to achieve the goal stated here, each ability triggered this way needs to be countered or otherwise leave the stack before it resolves and creates a delayed triggered ability (C.R. 603.7a; only if it resolves are its instructions followed under C.R. 608.2c).
EDIT (Dec. 9): Deleted second sentence in answer 2.
EDIT (Jan. 19, 2018): Changed a rule citation to conform to changes in the Magic Tournament Rules with Rivals of Ixalan.
EDIT (Jul. 6, 2018): One rule was renumbered with Dominaria.
EDIT (Jul. 14, 2018): One rule was renumbered with Core Set 2019.
EDIT (Mar. 17, 2019): Correctness edit.
EDIT (Jan. 25, 2020): Edited, including because some rules were renumbered with Core Set 2020.