You have to allow access out and Server (in) for it to work properly. I know that some firewalls use different terminology, and I haven't run ZA for 9 months, but as far as I am aware it needs to act as server.
IE is a Server - it goes into the "Trusted Zone" (your internet connection) and does it`s stuff! When you installed Zone Alarm you skipped an option to Allow "your default" web browser access - hence the messages. Tick the "remember this setting?" box and Allow.
I'm not suprised!, all I can tell you is that I run F Secure and IE is allowed as server in, I used to run Sygate and if you set it not to be allowed as server, Sygate always changed it back to allow. I did run ZA and to be fair I don't remember having a problem. I'm afraid I can't tell you any more