Most worms, trojans, viruses and other items that infect your computer no matter what firewall you have. ZoneAlarm is a great firewall, very intensive at scanning incomming and outgoing communications. While this is good, it can also slow your Internet connection down. Since you're already infected, I would get a free virus scan at Trend Micro
A firewall is for keeping things out, or in- it won't necessarily stop a virus infection, for the most part because anything your downloading is typically from a "trusted" source, that your firewall is configured automatically to let everything through. You need a good antivirus program. I recommend Avast!
It's free, auto-updates, and has several different shields that protect you from things you download, and if even comes with a P2P shield- so you're protected there as well.
When it comes to firewalls, you shouldn't have any problem running two different ones at the same time, although it could cause conflicts.
Antivirus software- you don't want to run at the same time, because it will cause conflicts.