Opponent plays Fizz Trickstarter. I want to play Disposal Order. When can I respond? When opp plays Fizz or when he chooses a card to play from trash? And what next? I play Disposal Order and he chooses another cards?

You respond when Fizz's "When you play me" trigger goes on the Chain — that's the moment your opponent declares which spell in their trash Fizz will play (FAQ #10020, #12050).

You could technically also fire Disposal Order while Fizz is still a pending card on the Chain (it's a Reaction, so Closed State is fine), but at that point the trash target hasn't been chosen yet, so you'd be guessing — and you'd be wasting your spell if they pick a different card.

When your Disposal Order resolves, you pick the up to 3 cards from their trash — not them. So you recycle the targeted spell (plus up to 2 others of your choice), and when Fizz's ability resolves it finds no valid target, so the "play that spell" instruction is ignored and nothing is played (Rule 359.3.e.7). The opponent can't swap in a different target — targets are locked when the trigger was placed on the Chain.