Is there a way to trade between characters on the same server? For instance, if I have my main doing blacksmithing, can I have a character doing clothcraft as well and trade between the two for materials and/or armor purposes?
Yes, as long as they are both Alliance or both Horde you can just mail the items between the characters. The only limitations are 1) you can't mail from Horde to Alliance or vice versa 2) you can't mail soulbound items. Mailing an item costs 30 copper (ie very cheap) and delivery time is one hour to anywhere in the world.
Nothing is tradeable between realms, best way to think of it as each realm as its own universe and there are a bunch of parralell universes, but who knows those crazy gnomes can do anything...