I assume your PS3 needs to open ports on the firewall. At least that's been my experience w/ most consoles if you intend to support online gaming. Problem is, you don't control the university firewall. Even if you could, it would only work for ONE user since the necessary port forwarding can only be directed to a single IP address (and even that IP address is most likely dynamically assigned). Until and unless you can solve those problems (highly unlikely), the router (as least when it comes to supporting the PS3) is a moot issue.
As far as using a router for general purposes, you will probably have to clone the MAC address of your PC/laptop (the one already authorized on the university network) to the WAN port of your router (a feature available w/ most routers these days). The university system will then be fooled into thinking your PC/laptop is connected to the system when in fact it’s your router.
How not to be detected? I suppose a strong wireless signal emanating from your dorm isn’t a good idea. Wouldn’t hurt to disguise the router a bit either, although ultimately it can always be found via inspection by simply following the ethernet cable back from the wall. Obviously I have no idea what is and isn’t a likely scenario on your campus. There’s also the possibility (if unlikely) of the university using traffic analysis to detect the router. Outright detection isn’t easy (unless you do something stupid), but they *might* be able to at least suspect a router is in the mix based on what it’s doing, where it’s going, or just the sheer amount of traffic it’s carrying compare to those not using routers. You can at least undermine some of those analytical tools by using a VPN (which encryption your traffic), perhaps one established back to your home (saves some money compared to a public VPN service). Another possibility is to use your PC/laptop as the router. IOW, use something like ICS (Internet Connectio Services) under Windows. That’s a software based solution as opposed to separate, standalone router. Now it appears as if your PC/laptop is connected normally. Someone comes into the room and as far anyone casually examining the situation can tell, you just have your PC/laptop connected as normal. But in fact it’s “configured” as a router. Or if you wanted to risk establishing a wireless AP, use something like Connectify to create a wireless repeater.
Ultimately there are no guarantees. Nothing stops the university from simply engaging in physical sweeps of the area if they feel so inclined.