what do you mean other computers? home computers or school computers? The school computers all probably use the same external ip so i don't know if that will help.
home computers, indeed.
it's common for schools to impose limits.
I'm just taking a quick look at the log and it says that the school pc connected at least 50 times, each time with a different port.
the client port always changes, it's normal. It's the server using a fixed port.
And if this always happens when there's no data excanged for a while, then how come my friend could connect to it 3 hours later from his home pc?
just ignore it, it's not a problem, it's normal. That's what all web servers do, it's in the nature of http.