Yes and Yes. The Thief has no restriction on what can be cast (other than "the exiled card") so you choose how you want to cast it as you cast it. Then, since you sent it on the Adventure, you (the Thief's controller) get to cast the creature. Just note that it no longer benefits from Thief's effect regarding the mana that can be spent to cast it. You will need to pay the cost with the right type of mana.
So the thief attacks and exiles some adventure cards (Giant Killer).
Can the thief's controller cast the adventure side? If so what happens when he does? Can he cast the creature side after as well?
Thanks