Is it possible for an alliance character to learn new languages.. say.. horde common language?
no
I swear at one point (back in like.. 1.2) I saw a troll speak Common, sitting in Goldshire on a RP server, organizing a world PvP event or something.
But it might have been a GM, though. It's not normal for them to do that, but I actually think I recall his name having a tag next to it.
I belive its possible to in the new Instance World Tree.