Dumbledore gets the map from the twins, doesn't give it back and the twins don't remember about it anymore. So, we know who'd obliviated the twins. However, we don't know the results of D's "find Tom Riddle" order... Also, the twins must've known about Harry's time travels by way of the map?

We have been prepared for the idea that Quirrell has any number of identities, multiple times.

Chapter 59:

"How many different people are you, anyway?"

The pale man lying on the ground didn't laugh, but from the broomstick Harry's eyes saw the sides of Professor Quirrell's lips curling up, the edge of that familiar sardonic smile. "I cannot say that I bothered keeping count. How many are you?"

Chapter 86:

"There's Dark Wizards that have one name. There's Dark Wizards that have two names. And there's Dark Wizards that change names like you and I change clothes."

Ok, my head hurts, what is going on with Quirrell?

1. Where is the real owner of Quirrell's body? I mean his personality.
2. Who is the Defense Professor? One would think Voldemort, but what is this David Monroe business then? And was the person who "returned from Albania" a real David Monroe? Or could it be just another mask of Voldemort (himself his own spy, why not?)
3. The body of QQ is destned to die. Is the time of his inhabitant also up? I doubt it.