I don't know whether or not Patti greets fans. She has in the past, though. Lincoln Center Theater has one general stage door for both the Beaumont and the Newhouse. When you're coming up the stairs from the Newhouse, exit through the first set of doors on the left. Then make another left -- as if you were walking towards the street -- and the stage door is right there. It's clearly marked.
Yes, exit through the glass doors and wait in that corridor. I was there recently. There weren't a lot of people. Everyone signed though Michael was in a bit of a rush and Patti ran by without really stopping. Someone else said that she might have recognized a stalker (not me!) and taken off because of that.