Colored squares look too clickable, maybe a list is better in this situation
It would be cool to have an achievement system, where you can show off badges on your profile (more of an UX thing)
Allies can be a problem if you've tutored/been tutored by a lot of people, also I don't really see the value of it. As another user I don't really care /who/ they've tutored, just how many and how well.
My thought process is that you'll only be viewing the profile during the session to get an idea of who your tutor/student is, so the goal of the profile page is to show the tutor's fields of expertise and experience (shown through achievements or stats). It has to be really simple so it won't distract the student from the tutoring session.
Something for the future: recent feedbacks and overall feedback