All the people telling me that BC, Wrath, and Cata had bad launches in yesterday's comments: they didn't for me! I played to my heart's content at midnight. Guess you were just unlucky.
Will I be able to send my heirlooms to the Pandaren starting zone on Tuesday, or will I have to wait until I choose Alliance?
No, you can't send heirlooms (or anything at all) to Pandaren who haven't yet left the Wandering Isle.