This is really two questions and aren't really handled well by a single program.
The antivirus question is easy, you'll be wanting ClamX. It is an OSX port of the venerable ClamAV engine. It is widely considered to be the default AV for Unix/Linux systems.
For your other question, free utilities that have good Mac integration may be hard to come across. The best tool I can think of would be a software firewall called Little Snitch. Since you can have it ask you to approve connections, as well as define what applications are allowed to talk to where, you might be able to accomplish what you need.
Now, with all that, keep in mind that if your computer is already infected, you can't trust the output of either of these applications. Clever viruses will just bypass the applications and continue working anyway. Applications like this are really useful for preventing yourself from being compromised, or detecting lame infections.