This cannot be a serious question. No, you cannot sue the university.

you can, but no way to know what the police might do. You could get a PO Box.

Any business has the absolute right to limit what type of payments they will take. Get a receipt.

For ethical issues, speak to your state board. This is not a legal matter.

A lawsuit will likely cost more than the amount in dispute..............

Can a person face criminal charges even if no police was called at the time of shoplifting? Yes.

This is an issue for your parents to resolve..........................

If you are going to tell the cops you loaned someone to, for example, buy drugs, that would be a really stupid thing to do.

You will have to sue them and a judge will decide who they believe.

You should probably hire your own attorney.