Can a VPN hide you in a university network and how?

They won't necessarily know WHAT you're doing, but they'll definitely know that you're doing it.

I'll also offer up that if you feel the need to hide whatever it is you're doing, then maybe you should reconsider doing it in the first place. Sounds to me like you're trying to circumvent some kind of restrictions placed on the campus network, and that would almost certainly be grounds for them to terminate your network access. So either pay for your own separate Internet connection where you can do these things, don't do them at all, or be prepared to suffer the consequences when someone in the IT dept at the school starts investigating all this VPN traffic. Odds are they don't need a very high burden of proof to kick you off the campus network, and the very fact that you need to use a VPN almost certainly means the intended purpose is something not allowed by the university.

When setup properly a VPN will encrypt all your traffic and all they will be able to see is that you are connected to the VPN and how much bandwidth you are using. You would have to check the campus network policy to see if there are bandwidth limitations or restrictions against using a VPN. It sounds from your anecdote that he violated network policy against using filesharing sites, but it’s hard to say without actually reading the policy.