if i have 1 unit in bf1, and i kill it to use baited hook ability. I can play the card in bf1?

Yes — you keep control of bf1 through Baited Hook's resolution, so you can play the found unit right back there.

The kill happens mid-resolution, and while a chain item is resolving the game is in a Closed State; a battlefield only becomes uncontrolled when it's empty during an Open State (Rule 323.6, cleanup task 4). By the time the outstanding cleanup would check, the new unit is already pending on the chain, so control is never lost. The killed unit's current Might (including buffs) sets the size limit for what you can grab.