He was sent back to Oblivion, yes he is still a Daedric prince. He was bitten by the Avatar of Akatosh and was "killed" in the mortal realm thus being sent back to Oblivion, he is alive in his own realm but he cannot come back to the mortal realm.
I think you're right about that. I think we can safely assume that, yes, Mehrunes Dagon still lives, just that he was banished from Nirn and sent back to Oblivion. And since as I understand it, the dragon statue that the avatar of Akatosh became pretty much replaced the Dragon Fires as the thing maintaining the barriers that protect the mortal realm from Oblivion, he shouldn't be able to invade again, at least not in the near future, though being the Prince of Destruction, I'm sure he'll find more ways to cause trouble in the future. And I'd imagine that he'll be back to giving tasks to heroes who find his shrine and rewarding the, if they complete him in Skyrim.
In any case, this probably belongs in Cheats, Hints and Spoilers, since what happens at the end of the main quest is probably a pretty big spoiler...