Notice the fact that I said in a sense. In the beginning of time (Elder Scrolls), there were two beings one was Anu and one was Padomay (Sithis). These two are said by the scholars of tamriel to be all powerful beings. Padomay is considered to be evil and Anu is considered to be good.
It is also said (by sithis) that Anu is a static, unconcious being, but I won't get into that right now.
Anu and Padomay fought. The blood of padomay became the Daedra, since he was evil, and the mixed blood of anu and padomay became the Aedra, capable of both good and evil deeds.
It is possible for a Aedra to become a Daedra, so maybe thats what happened to Azura and the rest. It is also possible that they simply have their own motives for doing what they do that the mortals do not know of yet. The Daedra also feed off of the mortals that worship them and would gladly kill them all in an instant, as shown by Boethiah. All beings are spiritually immortal to some degree. When someone dies, they go to either Atherius or Oblivion where they spend eternity.
The reason why alduins soul was not absorbed is because Akatosh probably interviened to save the one who was to bring about the end of time. Just because the DB killed alduin, it doesen't mean time will never end. They basicly just put off the inevitable.
If you have no idea how the conversation got to this point, go here and look in the commentshttp://steamcommunity.com/sharedfiles/filedetails/?id=140135154&tscn=1376663662