I have a few questions...
1) Is the professor a real person?
2) Where does Sophie ultimately go?
3) Who was Hilde?

If anyone can answer these questions for me it would be greatly appreciated.

The professor is not a real person, he is character of the book Hilde's father wrote for her birthday. Sophie is also a figure in that book. She is not going to go anywhere. At the very end of the book, you experience that the characters find that out and they live forever and stay where theyt are, how they are.
I would strongly recomment you to read the book.I am actually not the kind of person who encourages cheating. Today is your lucky day.