Rule #1: Whoever is paying the bills gets to make the rules.
All network traffic is logged by every device it passes through, from the wifi access point to the router to the web filter to the firewall. All of these are capable of generating extremely detailed reports.
Yes, they can see which PC (internal IP address) is connecting to which site (external IP address).
Yes, they can associate a specific PC (or any other device) with a specific user. There are a few ways to do that -- a service that runs on the computer, a network login prompt (username and password) for a wired connection, a login page on the Wifi network for your username and password, even the MAC address.
Yes, they can detect what protocol you are using. They can also detect P2P and VPN traffic, even when it's using nonstandard ports in an attempt to evade detection.
Yes, they can see that you're connecting to a VPN or proxy server.
If you're using HTTPS, at the very least they know the domain you are connecting to. With a little extra configuration magic, they can figure out exactly which URL you're visiting.
Yes, they can see how much inbound and outbound bandwidth you're using.
Yes, they can manage individual computers on the network to enable or disable features in real time.
Yes, they can receive notifications automatically for unusual or suspicious activity.
Yes, depending on the IT software and hardware your school pays for, teachers can see and record student screens, and take control of student computers.
Yes, they can record and archive every incoming and outgoing email.
The school IS your ISP for all practical purposes. They run the web filter, firewall, Wifi access points, routers, and everything else to do with your school network. The school has an upstream ISP, and that upstream ISP also has its own upstream ISP until you get to the "peer" level.
You (or your parents) agreed to all of this at the beginning of the school year. Enjoy the relative freedom as a student while it lasts. Once you graduate and go to work in the real world, you'll agree to all of the above (and possibly a lot more) as a condition of using your employer's computers and network.