To kill two birds with one stone, the answer to both of your questions is yes.
A Pokemon is considered Knocked Out if it has damage counters on it equal to or greater than its hp. It makes no difference whether the final damage was from an attack, a Special Condition, ability, or a Trainer card (such as Damage Mover), even if the damage was from yourself.
Well, as it says in the Pokemon TCG Rulings Compendium:
Whenever a Pokémon is Knocked Out, the other player gets Prize cards -- even if you Knock Out your own.
Source: WotC Chat (2000-02-10)
It doesn't matter who Knocked Out the Pokemon or how it was done -- if a Pokemon is Knocked Out, the opposing player always gets a prize card.
Sources: This and my own experience playing the TCG