Absol

If I use Absol's "Cursed Eyes" Ability to move three damage counters from one of my opponent's Pokemon to another, what happens if I choose a Pokemon with the "Theta Stop" Ancient Trait?

Since Theta Stop prevents all effects of Abilities done by your Pokemon, if you choose to move the damage counters to a Pokemon with Theta Stop the damage counters would be discarded rather than moved onto that Pokemon. However, if you choose a Pokemon with Theta Stop as the source of where the damage counters would be moved from, they simply are not moved and the Cursed Eyes ability stops there.

If my opponent has a Pokémon with only 2 damage counters on it, can I still use Absol-EX's "Cursed Eyes" Poké-POWER on it?

Yes, you can. If you use this power, you move the 2 damage counters to another one of your opponent's Pokémon.

If my opponent has more than one Pokémon with damage on it, can I use Absol-EX's "Cursed Eyes" Poké-POWER on one that has less than 3 damage counters even if they have another Pokémon with 3 or more damage counters on it?

You may choose to use Absol-EX's power against any Pokémon with damage counters, but if it has less than three you would move all of the damage counters off of it.

When using Absol-EX's "Cursed Eyes", do I have to move all three counters or can I choose to move less than three (like if I only need to move one counter to KO another Pokémon and wished to leave the other two where they are)?

You must move 3 from that Pokémon if there are 3 that can be moved.