I believe that Bjørn is keeping track of the experience for our Regents. I do not think he is keeping track of exp for any of the AA's and lieutenants...
As to what our characters are awarded xp for, I have no clue. Presumerably you got the most for going on adventure actions, perhaps you also gain something from ruling you realm. I'd hazard a guess that you also gain something from completing adventures.
Other than that, the exp rules are very much "black-box style" - we know we have them, we know something is happening with them, but we do not know how or what
Personally I agree with you that keeping track of exp for our characters would be fun, though not worth the hassle for other characters than your regent and possibly a lieutenant or two. An idea of what sort of things gives experience might also encourage us to seek those things out, so it could be used as a tool to encourage or reward certain kinds of behavior... which is how exp usually works. The default behaviors being overcoming challenges, killing monsters, "acting out" your character and so on.
I dunno though, I think the complexity level is high enough. I'd definitely be up for trying a more codified exp system.
Watch out though, in a moment
someone might come by and shout "AA and regents are not that important! The domain is your character!"
