I don't like the beta cuck MC, also hitting would get expelled but stealing money wouldn't? Also if the other girl was a witness they'd have long ago could have gotten him expelled. Heck all MC had to do was "mark" the money somehow and the tell the teachers and that'd be the end of that.
Considering she can touch things and the school introduced her she has to be a real person not a ghost. My assumptions are either she faked her death or she's someone who is impersonating the FL (Either a stalker for FL that wanted to become her or a friend that went crazy after her death either way it had to be someone who knew about MC). Also did his mother never tell her son his best friend died years ago? What a dick move.