Do I need to be worried about viruses/malware when I hook up my computer to my friends wireless network (via usb adapter)?
Do I have to disable my firewall to do so?
Any time you connect you computer to the interwebs you are subject to viruses, trojans, worms and other nasties. The method of the connection (wired, wireless, two cans and a string) is irrelevant.
Do not disable your firewall. There is no need to do so.
Can I catch viruses from their computer?
Reread my previous post.
Yes.
You can also transmit viruses from your computer to theirs, especially if they have fewer network security defenses against computers on the local network. Corporate intranets sometimes get viruses this way. Someone takes their laptop somewhere else and hooks up to another network, picks up a virus, and then transmits the virus to the intranet when they hook up the laptop again at work.