I play Void Assault, my opponent Gusts his minion, does Void Assault still resolve with me moving, i.e., is it "do as much as you can" like Starcrossed?

Yes, your friendly unit still moves. Here's the sequence:

1. You play Void Assault targeting your friendly unit and an enemy unit.
2. Opponent plays Gust (Reaction), targeting the enemy unit and returning it to hand.
3. Gust resolves first (LIFO) — enemy unit returns to hand.
4. Void Assault resolves: Instruction 1 ("Move a friendly unit") — your unit is still a valid target, so it moves normally. Instruction 2 ("Move an enemy unit") — the enemy unit is no longer on the battlefield, so that instruction is ignored (Rule 359.3.e.6).

The two instructions in Void Assault are not linked (FAQ #11529), so the failure of the second doesn't cancel the first. You do as much as you can — your unit moves, and the opponent's unit stays gone.