If students have registered their new address, they are entitled to vote in that constituency. Otherwise they would normally be registered back with their parents, and entitled to vote there, by post if they wish. It's quite possible to be registered to vote in several places, but it's an offence to vote in both of them.

No tax on voting - I think that would be seen as likely to force down turnout, which wouldn't be seen as advisable, since last time it was almost down to USA levels. On the other hand a tax on voting could bring in quite a lot of money, I wonder if anyone has thought of bringing it in...