What did he think of Mike?

We see that when Mike's bodyguards first describe to Vitelli the girl that hit Mike with the "thunderbolt" that he is furious. Then he comes back out of the house and Mike talks, sensibly, to him. He calms down and agrees to a meeting between he and Appalonia. So, at this point I'm not sure if he is afraid or he likes and respects Mike or what?

Mike makes it clear to him that he is an important person (albeit with a price on his head) and probably wealthy. Once he demonstrated that he showed the proper respect and that he wanted to court his daughter in the Sicilian tradition, Vitelli realized his daughter had a chance to marry into money. I think the novel goes into greater detail about Vitelli checking out who Michael was.

oh ok... thanks DT... it seems that I just need to go ahead and finish the novel as all the things I wonder about are in the novel. :-)

Exactly. The novel states that Vitelli observed the respect that Fabrizzio and Calo showed Michael and how they openly carried their lupare. It also says that Vitelli would check him out and if anything Michael said or implied was false, he could confront Michael with his sons and their own lupare.

I think that Vitelli realizes that he is Vito Corleone's son though it is not spelled out there. And knows that he is a man of great influence and that he could also get hurt.

It's one of the subtlest scenes in both the book and the movie (and one of the best-acted). What always strikes me about it in both places is that Michael admits he's a fugitive from the law--but Vitelli doesn't think it's a disqualification for Michael to be a suitor to his daughter--a real Sicilian touch. And the novel points out that Vitelli is willing to let Michael visit because he thinks he could be one of those "wild strokes of good fortune that Sicilians believe in" (not the exact words). That scene in both the film and movie had real conviction behind it.

I especially liked when, once Vitelli was convinced of Michael's sincerity and bonafides, he put on his suspenders. Classic.

Great non verbal ad-lib. Very natural.

I love the Sicily scenes. They are so authentic. FFC perfectly captured the essence of the island. How beautiful it is, how primitive it can seem. The actors spoke authentic dialect, too.

Those scenes always make me want to hop a plane to Palermo immediately.

Here's the quote: "But something told him this was one of those wild strokes of good fortune that Sicilians always believed in, something told him that his daughter’s beauty would make her fortune and her family secure."

Sorry, if I have to disappoint you. FFC told him to do the suspender trick.

Yes, but it was a great touch in a brilliantly acted and directed scene.