Someone tell me if I'm missing something, but when I kill critters, monsters, etc, I get no indication that I gained any experience, or anything else for that matter (other than looting). So apparently we do not get xp for killing critters ? Thus, we can only level up via questing ?

You get experience for kills. Quite a bit, actually.

This is the wrong forum for this, though.

This isn't the beta forums, the link is in your invitation email and there's information in the public beta thread created by a zenimax staff