I play Jayce "Man of progress" to kill my gear and play Vanguard armory for basically free (1 power) but my opponent react with starcrossed, does my Jayce full effect get in chain (Kill a gear, play for discount 7 energy) or what happens?

Yes — Star-Crossed resolves first and bounces Jayce, but your Jayce trigger is already on the chain and resolves independently of him (FAQ #8020, #6992).

Sequence: you play Jayce, he enters, his "when you play me" ability triggers and goes on the chain. Opponent reacts with Star-Crossed, returning their unit and your Jayce to hand. Star-Crossed resolves first, then Jayce's ability still resolves from the chain — nothing in it references Jayce's location or needs him on the board ("kill a friendly gear" is relative to you, the ability's controller, and is executed on resolution). So you may kill your friendly gear, and if you do, you get the permission to play a gear with printed Energy cost 7 or less from hand this turn, ignoring its Energy cost (still paying Power). Vanguard Armory's 1 Power is on you either way.

Two things worth flagging. First, if the gear you kill is a Gold token, killing it via Jayce's "if you do" instruction gives you no Power — the Power only comes from activating the token's own ability, so line up your 1 Power from somewhere else (FAQ #12537). Second, Jayce going back to hand doesn't waste anything: if you replay him later that turn you get a fresh trigger.