In the settings section for Zonealarm you can turn off the alerts that someone is trying to access your computer and I would advise you to do that as its only telling you that it is doing its job and you can get a bit paranoid when you get loads of reports about blocked attacks if you are into p2p downloads then you will get some of those.

However you should think about getting rid of Zonealarm as a much better free firewall is Comodo this scores higher in reviews of firewall software and is recommended by a number of pc magazines. For a very good free antivirus use AVG its a lot better than many you have to pay for and doesn't eat up system resources like some.