I would say that the safe zone isn't really a general purpose browser usage as it is isolated from the system.
I would guess that avast's Web Shield can still monitor the http traffic as normal, but if you are visiting banking sites that you use https (secure encrypted connection) then no.
I'm not sure what it is that you mean by "can the ISPs still track/look at our internet when using safezone" ?
The safe zone isn't some sort of anonymous proxy, it is just isolating your safe zone desktop from the rest of the system to prevent infection not so much anonymous browsing. Most browsers have a Private Browsing feature, but that just stops the recording of your browser history, etc.
Your ISP sill has a record of your IP address to be able to serve up the pages that you visit and the time, etc. So it isn't that easy to cover your tracks, why you would need to do that (strange request for your first forum post), as they say if you aren't doing anything wrong what have you to hide