Number 3 is correct and is what I've always used.
#1 seems kind of ridiculous to me--I would think that the person forgot to close out the first paragraph, then I would have to wonder why the second paragraph is so weird like that.
#2 would have me scratching my head that the speakers have been switched, yet the same conversation is just kind of being carried on. So weird.
Anyways, #3 is the way to be. But no matter what way you choose to write your stuff, the suggested thing is to keep it consistent. Pick what you're going to do and go with it the whole way through. That way, if you're doing it wrong, people start thinking you're doing it that way on purpose
