The PC side (running within Parallels) can get a virus, just like any other PC. What you should do is to do no web browsing on the PC side, just on the Mac side. It will be MUCH safer. But if you download things an run them on the PC side and not use it for apps you've purchased then those apps can have virus' in them even and you can be infected that way. I have never heard of a virus that can jump from the PC to Mac; mostly because they run different executables.
With any thing like parallels or fusion you can copy the image and use that as a back up. Thus if the image you're using gets infected, you can just copy the older version back and not have to restart from scratch.