Even though your computer has an antivirus, spyware, firewall program installed, it doesn't mean you are fully protected. Users still get infected all the time using Nortons, Mcafee or any other paid antivirus program.
Yes, its possible. All depends on the type of infection the other computer has. Do you have file sharing setup on both computers? I would disable that if so.
Just takes some common sense when browsing online. No porn sites, don't open emails from senders you don't know. Url links in emails from people you don't know are bad.