My main realm is Thunderhorn (PvE). I'm pretty sure I lack the patience to quest in a PvP realm. All I've heard are horror stories!
Do you know if both factions can be a deathknight? I'm alliance and made one, can Horde do it too? My initial guess is yes?
You sure can. They just can't be on he same server. Only one DK per realm. 

Olympus
Single & Not Looking
I've done this a few times as well. A lot of my friends play WoW, as I later learned, but none of them on the same realm. I think I've memorized the starting area by now.
Which realm are ya on again? The main realm I'm on is Tichondrius (pvp), and I have a few on a pve server too, Malygos. I'll probably end up moving at least the 60 Warlock over to Tich if I stay past this trial again. Pvp servers are just a lot more fun.