If I wanted to send an email to someone in a superior position (in this case, a professor), would I head it with [Professor’s surname]様? Or would ~さん be more appropriate?
Also, in the footer are there phatics like “sincerely” that people use, or is it more normal to sign only with your name?
■■先生 would be the appropriate way to address a professor in an email. It’s also customary to end the email with something along the lines of お忙しいところ恐れ入りますが、何卒よろしくお願いいたします, with a few variations depending on the situation.
There’s a couple of online sources with sample emails for various scenarios when writing to a professor, e.g. Townwork’s 教授へのメールの書き方と文例が丸わかり.