...I have an ASDL connection which is connected to a wireless hub... (bearing in mind, although different computers, they share the same IP address)
Actually, each of the computers will have its own, unique IP if they are all connected to the same network at the same time. From your description of your setup, it sounds like you have a router, not a hub; a simple hub won't allow multiple machines to simultaneously connect to an ADSL modem. Of course, the modem itself could also be a hybrid, containing not only the modem but a router as well.
Regardless- some of the basic answers to your questions are:
* The gaming PC isdefinitely vulnerable, just by virtue of it being on the network, and especially because the network also connects to the Internet as a whole. Keep in mind that even a fresh installation of Windows (with no other programs installed) will leave your computer configured with a number of running services which open ports on the machine through which network-propogated infections can enter. Additionally, because you have no antivirus or firewall software installed, the gaming machine is essentially open to intrusions.
* You don't really have to worry about spyware and adware programs themselves propagating from one machine to the rest of your network, as that is not a behaviour that those types of malware have. If the gaming machine is never used for Net browsing, its chances of picking up a spyware/adware infection are greatly less than that of the other computers.
* Worms do use the network propagation method of infection, which takes us back to the antivirus/firewall issue.