Gengar

If an opponent's evolved Pokemon is Knocked Out while Gengar is Active, does the "Catastrophe" Poke-BODY put all of the evolution stage cards and Basic Pokemon card in the Lost Zone, or just the highest stage Evolution card?

The evolved Pokemon and any of its pre-evolved stages and Lv.X cards go to the Lost Zone, and all attached Energy, Tools, etc. go to the Discard Pile.

If I use an attack that Knocks Out a defending Gengar with the "Castastrophe" Poke-BODY, but it also knocks itself out, does the attacking Pokemon go to the Lost Zone, or is "Catastrophe" no longer in effect when Gengar is KO'd?

Since both Pokemon are KO'd at the same time, Gengar's Catastrophe Poke-BODY is still working at the point when Knock Outs are evaluated. So the attacking Pokemon would go to the Lost Zone.

If my Active Pokemon does an attack that Knocks Out an opponent's Pokemon, but also switches my Active Pokemon to the Bench, would the Knocked Out Pokemon go to the Lost Zone if I bring up Gengar with the "Castastrophe" Poke-BODY?

Yes. Gengar is active at the end of the attack when Knock Out conditions are evaluated.

If I use Gengar's "Hurl into Darkness" attack, can I put a LEGEND Pokemon card (the top or bottom half) in the Lost Zone?

Yes, you can. Each half of a LEGEND Pokemon is treated as 1 Pokemon card.

If I use Gengar's "Cursed Drop" attack, can I put damage counters on more than one of my opponent's Pokemon, or do I have to put all four counters on one Pokemon?

You can put the 4 damage counters on their Pokemon in any way that you like.