Miraak is a dragonborn and a particularly powerful and power-driven one. He'd simply seek to extend his influence and grow in power.
I wouldn't worry about the dragonborns soul, he might be an avatar of Lorkhan himself whilst having the will to resist Mora's influence. Frea say that Aka made you for a reason, and that you can resist Mora. Given the Skaal's obvious secret knowledge and power I would suggest trusting Frea on that one. Not to mention that Miraak apparently needed your soul to leave, and that you gained his soul instead.. which might have put you over the top, so to speak.
This, more or less. Essentially Herma-Mora gave us a taste of the 'dark-side' when he helped us to beat Miraak and we're by no means his servant right now. However, as both Frea and Neloth suggest, you need to be wary of being lured into his service. Pretty a-typical of the Daedric Princes and fantasy literature as a whole (Lord of the Rings, for example).
Well, true, but I can't help but think of how many of Hermaeus Mora's boons you can receive from the Black Books throughout the dlc, and my mind is drawn to the example of Kodlak and his ties to Hircine. He was able to be freed, and his tie seems more powerful than the ties that HM has to the PC, but still. That seems to be how HM lures a mortal into his service: lots lof little tidbits that keep you coming back for more. When do you become his servant? At what point are you so inextricably bound to HM that his claim over your soul is absolute?
As for his being an incarnation of Lorkhan, how do you figure? I understand that he's dragonborn, but that's a special gift given by Akatosh (or potentially inherited in special cases like the line of Tiber Septim). I do agree, though, that his will is enough to resist HM's influence, but I suppose my question is how much and how long can he resist? I simply find it suspicious how easily Hermaeus Mora allows you to leave his realm so freely. Ostensibly, it's to let you be his representative or champion on Nirn, but he basically hands you the keys to Apocrypha at the end, and with each Black Book you find and read. Why would he allow such a powerful mortal such freedom unless he knew that mortal's soul was his? A daedra does have eternity to wait...
Of course, it does seem easy to defy a daedra prince. Look at Azura's Star: with a bit of sorcery and some soul-murder, it can be transformed into the Black Soul, something so far from Azura's will that it can't be anything but a corruption of a part of Azura herself. Same with Malkoran's twisted use of Dawnbreaker, and Erindur's dismissal of the Skull of Corruption from Tamriel. Still, these are artifacts, and while artifacts are physical representations of each daedric prince's will, that aren't the deadric princes themselves. Just how easy is it to defy them directly?