Spyware can still be easily installed with that firewall up. You still need to eject the spyware and use software that isn't being exploited such as Internet Explorer. Try Firefox or Mozilla.
I just downloaded the free version of Zone Alarm firewall. I also have SpySweeper, AD-Ware and AVG 6.0.
Do I need to keep SpySweeper now that I have the Zone Alarm? Am I confusing the function of each of them?