MrNateGate :
Rookie_MIB :
The basic problem as I see it so far is that you need to use their infrastructure, and you don't have access to some of the key parts. That limits you somewhat. How widespread of a game server are you talking about?
So much depends on how they set their system up.
As for privacy, look to a VPN. There's no way around the fact that your data has to traverse their wiring which they can then monitor, but if you use a VPN then it'll be encrypted and they won't be able to access any of it.
Just a basic server for a game like say, Minecraft or Ark Survival Evolved. I can run it from my PC quite easily, I just need to be able to forward the ports. Obviously students are not allowed to access the University modem, which is locked by a firewall, so forwarding ports that way is out of the question. That's why I am looking for a way to setup my own private network, through theirs. All I have to work with is an ethernet cable in my dorm...is there some device I can use to reroute this into my own private network?
VPN you say? You mean like TOR browser, would that work? Where do you recommend I get one, got any useful links?
You are probably not going to be able to port-forward anything. That's all done at the router level which is managed by the university.
As for VPN, it's similar in some regards to the Tor browser as it runs on a similar principle.
Tor is like going into a tunnel with multiple random exits. Each of your data packets goes in, then each packet comes out from a completely different node. It becomes impossible to track since you can't monitor all the exit nodes at the same time.
A VPN is different. Your computer creates a secure tunnel to a computer somewhere else, and the data inside the tunnel is encrypted. When it exits the tunnel it's decrypted and goes on it's way. Meanwhile, the exiting data is mixed with data from anyone else using that particular exit point for the VPN. People who watch the data from your computer to the exit node can't read it due to encryption. At the exit point since they don't know what data belongs to which person they can't do anything about it either. As long as the VPN doesn't keep logs (most don't), they can't match the data to any user.
Tor is free. Some VPNs are free (but their data rates are slow because everyone uses them), some cost a nominal amount ($50/year), those are usually better and more secure (no logs).
I'm really not sure what you can do about your port forwarding issue. Theoretically if you're getting a static IP, you could:
get a router, hook it to the ethernet port using the WAN port (the one that usually faces a public network)
clone the MAC of your computer to the router (many have this function built in)
hook your computer to your router
trick the university router to assign your router the static IP address (it usually would use the mac address which you cloned to 'remember' your device and assign it a specific address).
use the port forwarding on YOUR router to pass the specific packets to your computer.
This may or may not work BTW. I can't see them blocking ports on their network since so many college students do gaming and they need those ports accessible, so they might leave them open. On the other hand, putting a server on their network will piss them off most likely and if they detect tons of traffic coming in to your IP address they might lock it down.