Flash

My opponent plays Elder Dragon and targets my two units at the two battlefields, as well as one of my units in base. If I play Flash in reaction, moving the two units at battlefields to base, will they be dealt damage?

They will not.

Elder Dragon's play effect has a number of targeting restrictions equal to the number of locations on the board. Its controller chooses up to one enemy unit at each of those locations to target with the ability and each of those units must follow their respective targeting restriction. It is the equivalent to saying "Deal 1 to up to one enemy unit at battlefield A. Deal 1 to up to one enemy unit at battlefield B. Deal 1 to up to one enemy unit in your base. Deal 1 to up to one enemy unit in Opponent A's Base. ..." Each of those targeting restrictions is fulfilled separately for each unit targeted.

If you play Flash in reaction to the play effect of Elder Dragon, any units that are moved to a location other than the one where they were targeted will no longer fulfill the targeting restriction of the Elder Dragon play effect and will be unaffected by the ability as it resolves.

I play Alpha Strike targeting my Master Yi, Unstoppable and splitting 12 damage among three of the four enemy units at battlefields. If my opponent plays Flash in reaction to my Alpha Strike, moving two of the targeted units to base, can they then play Repulse and counter my Alpha Strike?

No, they cannot play Repulse targeting your Alpha Strike. (Except if both of the other chosen units have changed to a non-board zone, such as via the effect of something like Grim Apothecary's play effect, Heedless Resurrection's additional cost, or the instructions of Thrill of the Hunt.)

A spell that targets a game object creates a targeting relationship between it and the targeted game object. As long as that targeted game object remains on the board, that relationship is maintained even if the target no longer fulfills the targeting restrictions of the spell. Even if the units in this example aren't at a battlefield anymore, they are still being chosen by Alpha Strike. We know this is true because the spell remembers that it is targeting those units if they happen to fulfill its targeting restrictions again per rule 359.3.e.3. The only exception to this principle is if the units change to a non-board zone-in such a case, they are no longer the same game object and any relationship between them and the spell that targets them is severed. Even if they returned to the same battlefield, they won't be legal targets and the spell won't be choosing them.

359.3.e.3.If a target ceases to meet the targeting requirements while the spell is on the chain, then meets them again, it's a legal target.

It can help to visualize Alpha Strike's targets with a colored arrow pointing from Alpha Strike to those units. Even if the units move to base and are no longer legal targets, they are still being chosen by Alpha Strike; we can imagine that the arrow is greyed out, but still present. Meanwhile, if they moved to a non-board zone the arrow would disappear entirely, since the game object it is connected to no longer exists. Repulse cares about the number of those arrows that point to friendly units, not the color of the arrows.

What happens if my opponent plays Flash on their Akali, Silent that's currently in combat after I play Star-Crossed targeting her?

Star-Crossed will resolve to no effect.

Akali, Silent is what the rules refer to as "untargetable" for enemy spells and abilities when she isn't in combat; meaning she is not a legal target for them. Enemy spells and abilities being played when she's untargetable since they can't choose her. If she becomes untargetable after she's already been chosen by an effect and retains it as that effect begins to resolve, it will "mistarget" her. She will be unaffected by any of the spell or ability's instructions. If an instruction chooses only her, that instruction will be ignored.

Relevant Rules: 757.1., 758., 758.1.

- If a unit at a battlefield says "I can't be killed." and a player plays Hidden Blade choosing that unit, the unit's controller will still draw 2 on resolution of Hidden Blade. (The instruction was negated and not ignored, so the linked instruction will still execute.) - If a unit at a battlefield is chosen by Hidden Blade and in reaction its controller plays Flash moving it to base, that unit's controller will not draw 2 on resolution of Hidden Blade. (The instruction was ignored, so any linked instructions will be ignored.) - If a unit at a battlefield is chosen by Hidden Blade and in reaction its controller plays Zhonya's Hourglass, that unit's controller will draw 2 on resolution of Hidden Blade. (The unit is on the board and can have its information checked, and the instruction was negated and not ignored.) - If a unit at a battlefield has been affected by Smite previously this turn and it is chosen by Hidden Blade, that unit's controller will not draw 2 on resolution of Hidden Blade. (Although the instruction is executed, the unit is not on the board to have its information checked. Additionally, the unit was moved to a non-board zone by an effect other than Hidden Blade and thus no longer has a controller that Hidden Blade can reference.)

359.3.e.5. If any of the spell's targets are no longer legal, those game objects, players, or zones are unaffected by the spell as it resolves. Any instructions related to an illegal target can't be followed. Example: A player plays Void Seeker, a spell that says "Deal 4 to a unit at a battlefield. Draw 1." The unit's controller uses a Reaction to move the unit to their base. Since the unit is no longer a legal target, it is not dealt any damage. Void Seeker's controller still draws 1. Example: A player plays Bellow's Breath targeting a unit in combat that reads in part "I can't be chosen by enemy spells and abilities unless I'm in combat." In reaction, that unit's controller plays Flash, moving the unit to their base. The unit is no longer in combat, so it is no longer a legal target for Bellow's Breath. The unit will be unaffected by Bellow's Breath as it resolves. Example: A player plays Hidden Blade from the facedown zone at a battlefield, targeting an enemy unit. In reaction to Hidden Blade, their opponent plays Tideturner from facedown at another battlefield, choosing to swap locations with the unit Hidden Blade targeted. When Hidden Blade resolves, the chosen unit is no longer at the appropriate battlefield, so any instructions related to that unit are ignored.

359.3.e.9.a. If another spell or ability attempts to reference the number of game objects, players, or zones that a Finalized Chain Item targets, it will include any mistargeted choices, but not any targets that have changed to a non-board zone. Example: When a player moves their Volibear, Furious to an occupied enemy battlefield and combat initiates, Volibear's attack trigger goes on the chain targeting three of the units at that battlefield. In reaction, the defending player plays Flash moving two of the three units back. That player cannot then target the attack trigger with Repulse, which reads "Choose a friendly unit at a battlefield. Counter an enemy spell or ability that chooses it and no other friendly unit." If the defending player instead played Heedless Resurrection twice, killing the two units, Repulse can legally target the attack trigger, because two of the targets have changed to a non-board zone.