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Hi i am a student in a school called Nørve VGS in Norway.
I attend to a class that mainly study computer electronics, and digital infrastructure. I can firmly say without bragging that i am one of the best students in my class, as computers have been my hobby the past 13 years. And my teacher asked me to soon become the assistant network manager, help the network manager do tasks, and also set up a test Skule-Linux(debian-edu) enviorment. A linux enviorment that hopefully will put to use on the whole school.

It is common to a lot of people in the Scandinavian countries do do a lot of file-sharing, trough Torrent's and other similar programs. And this (bad)habit has spread to students in school time, and as most people on the school has laptops, its not a easy task to stop the people polluting the network(it sounds easy, but the network administrator at least has not been able to track or stop this)

at the school we cannot control what programs the private laptops run, as the laptops are owned by students founded by scholarship from the government, so we cannot exclude laptops either.

The actual question.
So the actuall question is, is it possible to set up a virtual machine system on the private laptops. where the virtual machines run linux, and only programs run on the virtual machines have access to the internet. and also where the linux that run on the vbox has the user account located on a server on the school that unables the students to install/uninstall and run administrator commands or programs.
similar to or just like a thin-client.

or to do this do we have to have a live-cd system?

A huge thanks in advance

What I would do is to hand students Xming or maybe cygwin X or something like that (a Windows X server) and PuTTY - for Windows, and if anyone hopefully has Linux, 'ssh -X' will do. So just make them logins on server, and provide no routing. If anyone wants anything from school network, it is needed to login and then anyone can just use the programs - that run on server under their account - on the screens of the laptops. If you want to give them any rights on server - you treat them as ordinary users. Really I doubt that you can do a virtual Linux machine that would run on a students notebook so that it has Internet access and user cannot have the same for host Linux system. Note that if users can use compiler (or even advanced enough shell) they have positive chance of writing some kind of proxy and get their host OS on notebook online...

I would suggest you enforce network restrictions on the gateway/firewall and forget about the laptops.