Can I have the same app in TestFlight and Appstore with different versions without one overriding the other, I mean a users signs up for the Test version, and could he be able to have the AppStore version and the Test version at the same time, each of which should be independent, to avoid errors. Is this possible?
If you use two different Bundle ID's (with appropriate App ID's) for the App store app and the Test Flight app (or Ad Hoc distribution), then your user's iOS devices will treat them as two different apps (e.g. let both be installed, run them both side-by-side on iPads, etc.) But that essentially means you have two different apps, with two different iTC pages and build submissions, etc.
If the Bundle ID's are the same, iOS will only allow one at a time to be installed on a device.