Are falling star units choose on cast or resolve

Resolve, not cast — Falling Star has no targets when you play it. Its two "Deal 3 to a unit" instructions are reflexive triggers: the spell goes on the chain with no targets, then when it resolves it creates two triggers that you choose targets for as they're finalized on the chain (FAQ 4890).

That means an opponent responding to the spell itself can't know or restrict your targets yet, but once the triggers are on the chain with targets chosen they get a priority window before each one resolves — and each trigger is a separate chain item, resolved one at a time.