On the original point, of who the Defense Professor is, I saw a great idea on Reddit - the Troll is the Defense Professor.

“Not so,” said Dumbledore. “If Voldemort has not fully mastered the wards, then the wards had to believe that some Professor’s hand was at work. Else they would have cried out at Miss Granger’s injury, and not only upon her death.”

So if you need an agent in Hogwarts to kill a student, you want the wards to think that they're a Professor.

Also, about Quirrell stealing bodies

The smile that the Auror gave had absolutely no mirth in it. “So where’s the real Quirinus Quirrell, eh? Under an Imperius in the bottom of a trunk somewhere, while you take a hair now and then for your illegal Polyjuice?”
“You are making highly questionable assumptions,” the Defense Professor said with an edged voice. “What makes you think I did not steal his body outright using incredibly Dark magic?”