Is it permissible for him to take the money left over by the students after a trip because he was not paid anything for supervising?

Praise be to Allah.

You do not have the right to take anything from this money, because you have been entrusted to spend it for the purpose for which it was given, which is to take the students on trips. So it is not permissible for you to spend it on anything other than the purpose it was paid for. Allaah says (interpretation of the meaning): 

“Verily, Allaah commands that you should render back the trusts to those, to whom they are due”

[al-Nisa’ 4:58]

What you must do is to give the money back to those who paid it, or keep it for them so that you can spend it on the purpose for which it was paid. The fact that you do not receive any salary or remuneration does not allow you to betray the trust and consume wealth unlawfully. You should ask for your right to be given something in return for your work. 

You do not have the right to take anything from the fees paid for the study-circles either, for the reasons stated above. 

What you have to do is to fear Allaah and beware of all haraam wealth. I ask Allaah to help you and guide you and to grant you plentiful provision. 

And Allaah knows best.