Most likely the type of network would be a Lan. The school probably subscribes to
a main service provider, I dont know of hand if schools subscribe from a backbone
provider but that is possible.

As of Now:
1. The network is a LAN with a backbone provider, meaning there is a central
server(s)

2. The school has all the rights to block p2p software if they want to
most likely through port access

I hope I didnt misrepresent any information but thats what I personally know
do not take that as word of god.