Setting up a DMZ for your computer without a firewall is suicide. It would be analagous to sitting in the middle of a hackers convention and yelling out HEY MY COMPUTER IS INSECURE!!!!!!
If you are having problems with the application freezing or disconnecting after a certain period of time, i can almost guarantee the problem is not with the firewall. If it was, the application wouldn't work at all. What would be the point of a firewall if it only blocks traffic after two minutes?
The only thing the firewall on the Linksys router will do is block incoming connections, like if you were viewing someone else's webcam. Even without opening the ports on the router, you should be able to connect and talk to people without any trouble.
One possibility might be a loss of signal. If you have a lot of 2.4GHz phones being used or you're connecting through multiple walls or from a far distance, your messenger application might just be losing connection to the internet.
I would first try to re-install the application. If that does not work, try installing the application on you're roomates computer and see if he has a problem. If he does, you know the problem isn't with your computer, its something with the router.
You can also try using the application while you're connected with a normal network cable instead of being connected via wireless. If it works while you're connected via network cable, you know its something specifically wrong with the wireless portion of the router.