It was only with ZA Pro, then there have been previous conflicts with its privacy features, this however is usually only seen in pages like logon to yahoo/hotmail, etc and then the conflict caused nothing to be displayed. That shouldn't be a problem with ZA free.
There is definitely a page formatting error, in the past this was associated with non-ie browsers conforming to standards whilst pages were optimised for IE, now IE7 is more standards compliant there have been some sites where this caused some issues. However, this seems more severe than that.
Do you happen to use a proxy to connect to the internet ?
Whilst I don't feel this will have an effect it is certainly worth trying to at least confirm your avast installation is good. Try a repair of avast. Add Remove programs, select 'avast! Anti-Virus,' click the Change/Remove button and scroll down to Repair, click next and follow. You need to be on-line to do this.
If that doesn't work try, uninstall, reboot, install, reboot.
Other than that all I can suggest is trying another non-ie based browser Opera or Firefox with the web shield enabled and test the same pages and see what happens.
Last suggestion after all others:
You could disable the transparent proxy for the Web Shield but leave it running and manually set IE7 to use the proxy.
Use a text editor and edit the avast4.ini file, the default installation location is C:\Program Files\Alwil Software\Avast4\DATA\avast4.ini (I would advise you copy avast4.ini before editing it, just in case). Locate the line containing ZoneAlarmCompatibility= change the value to =1. Save the edited avast4.ini file. This can easily be reversed after the test by changing it back to 0.
Manual setup to use the web shield proxy. Whilst the IE tutorials relate to IE6, you should hopefully be able to find the same in IE7.
For IE - broadband users: -
Tutorial - Web Shield Proxy Set-up for IEFor IE - dialup users -
Tutorial - Web Shield Proxy Set-up for IE (Dial-up)For Firefox users -
Tutorial - Web Shield Proxy Set-up for Firefox