I don't think anyone else has discussed the certificate issue:
In my experience a lot of schools use a MITM firewall to intercept HTTP traffic for their filtering policies such as to look at the content of the page. This is a problem for HTTPS because they have to replace the certificate with their own - which is probably what they want to install.
See this vendor for example: http://www.rm.com/products/online-safety-tools/rm-safetynet/ssl-interception#downloads
I am assuming that is what the certificates which you are being given are for? There is no reason to give IT admin access when you can just install it yourself, its easy.
Installing will allow you to browse HTTPS but obviously bear in mind that they will be able to intercept and read communications, over any network that is controlled by the owner's of that certificate.
To avoid the interception you could probably run an encrypted VPN on one of their open ports 80/443/53 etc. and tunnel all your HTTP traffic through that. Just don't tell them because it is probably against their policy haha.