I am quite confused on some subjects and would like some answers. Firstly, there is Aetherius. Is Aetherius the home of the gods or not? Do souls that die go there and continue to live on as a spirit? Secondly, there is the matter of the Dreamsleeve. What is it and where is it located? Are souls recycled when the enter it? How does this process work?

No, Aetherius is not the home of the gods, if by the gods you mean the Aedra. They were bound to Mundus by creation. Souls don't go there after death, at least not in the sense you mean. I don't know how the dreamsleeve thing works so there's room for it in that idea.

I will answer to the best of my knowledge.

Aetherius is a realm of pure potential. It's about as Anuic as you can get in the Aurbis (The observable TES universe). If you read MK's http://imperial-library.info/content/cosmology (Which you should) you'll learn that the stars and sun are really tears in the Aurbilical fabric between Aetherius and Oblivion. Through these holes, the abundance of potential (magicka) shines, which is harnessed by many living things. The myths surrounding the sun are different in every mythology. Aldmeri myths state that Magnus (an original Aedra of magic and designer of Mundus) did not want to give up a part of himself to create the world and left to Aetherius, tearing a huge hole to get there. Either way, Aetherius is populated by Magnus and et'Ada (powerful spirits like the Aedra) dwell in Aetherius. The Aedra themselves dwell on terrestrial planets in the Aurbis, though they aren't in Oblivion. I'm not sure where they're astronomically located. As far as any of us know, mortal souls do not go to Aetherius upon death. Although you do get to visit there in the Daggerfall main quest.

The Dreamsleeve is where all mortal souls--unless bound to a specific Daedric prince, powerful sorcerer or some really important personal stuff (think ghosts)--go after death. The Dreamsleeve can be viewed as a sort of magical tunnel, in which a soul is vacuumed up, scrubbed clean for some period of time, and then tossed back into a fresh mortal. The Dreamsleeve has--as far as we know--no physical presence in the Aurbis, it simply Is. When a soul enters the dreamsleeve, they see whatever they want to see. A traditional Nord will, upon death, go to Sovngarde, their wench-filled mead-drowned battley heave, and so on.

That's--in a nutshell--the answer to your questions. If you need clarification please let me know. I also suggest you mosey around the Imperial Library (linked above). It contains literally every piece of information on the Elder Scrolls accessible to fans.