well firstly if you have norton then you don't need AVG, or vice versa, you only need one bit of antivirus software, running more than one at a time can cause problems.
No somebody should not be able to shutdown zone alarm from outside (it would be a pretty pointless fire wall if they could!)
If you suspect that somebody has done this then they must have access to your computer in some way, if they can gain access from outside then you have something very very nasty on your computer and you want to be running a full virus scan using either of the AV software you have and you also should be checking it for spyware using adaware pretty sharpish!