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Yes, it is. It's an account bound item.

CannabisCountryCIub - Alliance - http://cannabiscountryclub.org/
Hysteria - Horde - http://warhysteria.shivtr.com/
I'm in both of those.

Hysteria
http://forum.warmane.com/showthread.php?296315-lt-Hysteria-gt-Horde-PvP-Guild

Server xp rate?

I have had an instant queue on both alliance and horde. It's pretty much the same. One moment you wait 2-3 minutes other one you get instant queue.

Pvp/pve?
Horde/Alliance?

Do argent tournament dailies in icecrown. You'll get 2-3k + gold daily. You won't have to worry too much about getting ganked there.

CannabisCountryClub - http://cannabiscountryclub.org/
People do plenty of bg premades. Once in a while a rated bg aswell if there're any groups being formed on alliance.
You need 1.9k arena rating...

Mostly yes. Since in most cases as horde i have to wait 2 - 3 minutes for a bg to pop.

Difficult to say. My low geared shaman(horde) has 17 wins and 19 loses in total. I haven't been in any premades with him.

Both factions have similar population if i'm not mistaken.
Right now on horde i have to wait few minutes to get a bg however there're times when i get instant queues.
Regarding pvp, no idea since...

Horde has few minutes queue. Isn't instant but you won't be waiting forever.

I would say frostwolf since it's more populated and horde doesn't have any trouble with battleground queues.

When archeology(on mop) will get fixed?