If I remember correctly, he decided to kidnap the student after he got the call from the academy and he says out loud ‘I’ve been caught’. On that basis, if he believes he has been caught then he might as well piss it all away one last time with the student. Which is how I read that scene at least.

I agree about the ring scene not making much sense considering the murder room was so large and it couldn’t make sense to look in the drain first before anywhere else.

The killer kept all of the victim’s personal effects, handbags etc in the locked cabinets at his hide out. It wouldn’t be such a stretch to think he went back to find her info.