Realm/server choice

[Tizziel]

Does it matter which realm/server I pick for arena, open PvP and PvE?

 

 

[Yashuoa]

I would like to know this as well.

[Dracconus]

Because of the fact that the dungeon lobby is cross realm logic would say the arena is as well, so I'd say a safe assumption of no.
As for PVE, yes.  Population of your server directly affects your PVE ability especially with the new patch since the dailies at end game pretty much all require a party.