That would be creepy. My thought on that is Moses wrote those 5 books but after he was taken/died someone had to finish that very last part. Once he had been "taken", as Elijah and Enoch were, and they never saw Moses again (as God "buried" him) he would essentially be "dead" to the writer.
God had to be letting us in on that fact as He made it clear who was on the Mt. of Transfiguration with Christ.
As to why Michael is contending with the devil about the "body of Moses" I don't know. Maybe it's about his transfigured body. The bible does say Moses died but then we know he didn't as we see him in a transfigured state. It's something to think about.
Not necessarily. Samuel got to chit-chat with King Saul after he was already dead. (1 Samuel 28:15)