MTG Salvation

Sorry, guys, but I’m still confused here. I searched and searched but found no rules that say it’s possible to retain priority.

I quoted the rule. (See above.) If you cast a spell or activate an ability, you get the priority immediately afterwards, before anyone else does. "Retain priority" is a common phrase used to mean not passing this priority right away. Usually you're assumed to pass (also see above), because there is seldom a strategic advantage to not pass.

It is totally legal to play multiple spells without passing priority.

116.3c. If a player has priority when they cast a spell, activate an ability, or take a special action, that player receives priority afterward.

However, your opponent is considered to have passed priority in what you described. MTR4.2 states

Whenever a player adds an object to the stack, they are assumed to be passing priority unless they explicitly announce that they intend to retain it.

I'm not sure what "may I play just one card to respond all the spells at once?" means, but if your opponent does cast them without passing priority, and you cast something after that, it is put on the top of the stack, and it resolves before all other spells.

First, lifelink isn't a triggered ability, so missed trigger rules don't apply.

Creatures' P/T and abilities are derived information (MTR4.1), and, "players may not represent derived or free information incorrectly", which means while don't have to answer questions, you can't give incorrect answers. Also, life total is a status information, which is "information that must be announced upon change".
If your opponent knew it is illegal and was consciously doing it to gain an advantage, it's Unsporting Conduct — Cheating(IPG4.8) and your opponent is DQed. Otherwise, it is Communication Policy Violation (IPG3.7) and they get a warning.
While CPV allows a backup, it would be bad, as you stated, so you will probably continue the game from this point. For life totals, IPG says nothing explicitly, but the only option is to use the "correct" life total.
Oh, and saying "****" might be considered Unsporting Conduct — Minor(IPG4.1), depending on the situation.

Adarkar Valkyrie problem seems to stem from the ambiguity of the word "ability":

112.1. An ability can be one of three things:
112.1a. An ability can be a characteristic an object has that lets it affect the game. An object's abilities are defined by its rules text or by the effect that created it. Abilities can also be granted to objects by rules or effects. (Effects that grant abilities usually use the words "has," "have," "gains," or "gain.") Abilities generate effects. (See rule 609, "Effects.")
112.1b. An ability can be something that a player has that changes how the game affects the player. A player normally has no abilities unless granted to that player by effects.
112.1c. An ability can be an activated or triggered ability on the stack. This kind of ability is an object. (See section 6, "Spells, Abilities, and Effects.")

The question is : Does "causes a triggered ability of a permanent you control to trigger" mean
"causes a triggered ability(112.1a) of a permanent you control to create a triggered ability(112.1c)" or "causes a triggered ability(112.1c) whose source is a permanent you control to be created"? Adarkar Valkyrie's case is the latter but not the former. Of course, even if two instances of the triggered ability are created, it doesn't do much for the reason already mentioned.

As far as I know, there is no rule about what constitutes a meaningful change, so it's up to the judge. I'd say if there is a possibility that Gaea's Blessing isn't in the library now, then it is indeed meaningful.

It seems Natedogg quoted a wrong rule.

If an effect divides or distributes something, such as damage or counters, as a player chooses among any number of untargeted players and/or objects,

Biogenic Upgrade targets the creatures, so this doesn't apply. Fortunately, there is a comment:

(Note that if an effect divides or distributes something, such as damage or counters, as a player chooses among some number of target objects and/or players, the amount and division were determined as the spell or ability was put onto the stack rather than at this time; see rule 601.2d.)

Rule 601.2d is:

601.2d. If the spell requires the player to divide or distribute an effect (such as damage or counters) among one or more targets, the player announces the division. Each of these targets must receive at least one of whatever is being divided.

In short, you need to distribute at least one on each target, and you distribute as you choose targets. What OP wants to do is impossible on multiple level.

"One or more" usually comes after "whenever", to prevent abilities from triggering multiple times. If you're asked "Do you have a sibling?" and you have two, would you answer "no"?

If it weren’t for the Gatherer ruling, it seems like we would all be in agreement that I could indicate my choice in any manner I saw fit, so long as it prevented me from changing my choice (correct me if I’m wrong in that assumption).

I in fact disagree. Gatherer ruling is like reminder text and has no authority imo.

The Gatherer ruling itself seems to not necessarily apply, seeing as it says “without revealing it,” and was meant as the method for indicating a card when hands are hidden. So, are we sure that there’s no other way to make the choice other than to set the card aside, and therefore reveal the choice early?

I'm not interested in the physical process. From my understanding, the English word "indicate" implies "inform".

Literally the only card that chooses a card in a hand with no reveal is Master of Predicaments, according to a quick Gatherer search.

There are other cases where this is relevant. For example, when multiple players discard to Liliana of the veil.

That said, I agree with Horseshoe_Hermit.

400.11. Some effects instruct a player to do something to a zone (such as "Shuffle your hand into your library"). That action is performed on all cards in that zone. The zone itself is not affected.

This rule means "your hand revealed" means "all cards in your hand revealed". Card A is revealed, card B is revealed, and card C is revealed. "Clearly indicate" presumably means make it clear it's A, B, or C. Nothing indicates they can stop being revealed, so everybody knows what it is.

[EDIT]
Oh wait I see the renegade doppelganger becomes a copy of the body double. That works right?

That seems to work just fine.

"Minimum mana cost of 4" part isn't accurate, though. It reduces 1WB to WB, or 2(W/B) to (W/B).

If it leaves the battlefield and returns, it is considered a different object, so it isn't shuffled into the library.

601.2f. The total cost is the mana cost or alternative cost (as determined in rule 601.2b), plus all additional costs and cost increases, and minus all cost reductions. If multiple cost reductions apply, the player may apply them in any order. If the mana component of the total cost is reduced to nothing by cost reduction effects, it is considered to be {0}. It can't be reduced to less than {0}. Once the total cost is determined, any effects that directly affect the total cost are applied. Then the resulting total cost becomes "locked in." If effects would change the total cost after this time, they have no effect.

Basically, increase, decrease, and then Trinisphere. They have to pay 2U in both cases.

Wall of Roots with four counters on it already and a convoke spell or anything that sacrifices itself for mana and a convoke spell wall is just the only one that comes to mind that is actually tournament playable in a convoke deck already.

Wall of Roots is a good example, but sacrificing a permanent for mana isn't. (You have to produce mana before paying costs anyway.)

Scrap Trawler, Chromatic Star combo

This is a weird interaction and I wish it didn't exist.

Well, for one, convoke/improvise style cards, or anything with additional/alternate costs, get weird rules-wise if you generally pay costs before casting. Since now you’d be doing part of the cost up front, and part while casting

Activating mana abilities and paying mana are two different things. You can combine convoke and floating mana just fine.

The best example off the top of my head is cost changing effect (like affinity) or casting restriction (like legendary sorceries) and sacrificing things for mana.

"Whenever a Sliver attacks and isn't blocked, it gets +1/+0 until end of turn." is meant to describe "All Sliver creatures have frenzy 1", not "frenzy 1". The first two work similarly.