1. He has finished. (past participle--this one is used when you're focusing on the present result of a past action. The action is probably a very recent one (very close to present time).
Yes, I agree with Ivanhr that both are correct. Both refer to events that took place in the past. 1st - Present Perfect Tense (INDEFINITE time); 2nd - Simple Past tense (DEFINITE time = FINISHED [simple form]; DID FINISH {emphatic form] Thanks.