If I attach a Grass energy from my hand using M Sceptile EX's "Jagged Saber" attack to a benched Malamar EX, will I be able to use Malamar EX's "Hyper Hypnosis" Ability to put my opponent's Active Pokemon to sleep?
Yes, you can. An Energy is being attached from your hand to Malamar-EX, so Hyper Hypnosis can be used.
What happens if Zoroark uses its "Foul Play" attack to copy Haxorus' "Dragon Dance" attack? Would it apply to Zoroark or not (because its name is not Haxorus)?
Zoroark's Foul Play can choose Dragon Dance, but since its name is not "Haxorus" the attack will basically have no effect. Dragon Dance specifically refers to Haxorus, so any Pokemon not named Haxorus cannot receive the damage boost.
What happens if Mewtwo EX uses its "Damage Change" attack against a Pokemon that blocks effects of attacks? Does nothing happen, or does Mewtwo EX get to remove its damage counters?
Mewtwo-EX would remove its damage counters, but the opponent's Active Pokemon would not remove nor receive any. If you try to move damage *to* something that blocks effects, the damage disappears. If you try to move damage *from* something that blocks effects, the damage stays there.
Does a BREAK Evolved Pokemon such as Raichu BREAK or Marowak BREAK still have access to the type changes from Flareon's "Flare Effect" ability or Vaporeon's "Aqua Effect" ability or Jolteon's "Electric Effect" ability? Or do those Abilities no longer apply after the Stage 1 Pokemon becomes a BREAK Evolved Pokemon?
Pokemon BREAK are their own classification, so they are not considered Stage 1 Pokemon. Although BREAK Evolved Pokemon share many of the traits of the Pokemon it evolves from, it is no longer a Pokemon of the previous stage it evolved from. Since it is no longer a Stage 1 Pokemon, the Flareon's/Vaporeon's/Jolteon's abilities do not apply.
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.
Source:
TPCi Rules Team (2015-09-03), TPCi Rules Team (2015-09-24)
Must I have my Deck and Discard Pile on the right side of the field, or can I have it on the left side (it's easier for me on the left because I am left-handed)?
The standard play layout is to have the Deck & Discard Pile on the right side and prizes on the left side, but having them the other way around is also permitted.