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.
Source: TPCi Rules Team (2015-10-29)

Relevant cards

Note: All applicable cards may not be listed below.
BW1_71
XY8_111