XP is awarded after noncombat encounters, it just isn't displayed. This is something that needs to be fixed.
Wizards being able to learn spells of all classes from scrolls is an obvious oversight. It will definitely be fixed prior to the games' full release.
I couldn't see the XP total displayed anywhere on the character sheet screen, which I thought was odd. You never know quite where you are. Alignment isn't displayed either, which I rather liked. You can easily tell a person's alignment from their behaviour, but it's fun to see it roleplayed.
I had to search for the XP also. It's a slidebar under your character description. It has your current level on the left and next level on the right. Hovering over the bar tells you your XP, and how much you need to level up. It would be much better to see the numbers directly.
There's no alignment (yet) in the EA.