University students and professors! Especially U.S. top 50s! Help! Is this typical university professor?

Yes, it's very typical that professors won't tell you exactly what's going to be on the exam. That's why you're supposed to study for it. And it's very typical that they won't tell you the exact questions. Many students try to find out exactly what's on it so they don't have to put in any work; it sounds to me like your professor thinks you're one of those students. Just start studying the material.