It is unclear what the school says the certificate is for. It may be for WPA-Enterprise Wi-Fi authentication. It may also be for HTTPS interception. Please expand on that. Surely there’s some information on why you’re supposed to install the certificate…?
I will provide an answer about installing a CA certificate in the trusted root CA store. Going by the fact that it goes into the trusted root CA store, the certificate would not be unique per student.
There are two environments to consider. Your school network and other networks.
When you are connected to the school network, your school
- can intercept your connections, even when encrypted (see also last bullet)
- could accidentally leak the certificate’s private key
- can slow your web browsing either way
- can route your traffic any way they like, middle man or otherwise
Routing is unrelated to any certificates. Certificates are for trust. Having a CA certificate provided by the MITM installed makes security warnings go away, because you now trust the MITM.
When not connected to the school network
- the school cannot see where you browse
- the CA makes you more vulnerable (see above)
- browsing speed is unaffected
- the school cannot redirect or intercept your traffic
If you do not trust the school to properly manage this security-critical data, you should not trust their CA. This will probably make using their Wi-Fi impossible.