Well I hace read your ideas in multiple threads but I think that I will include mine here! Your ideas are awesome, but I have also a couple of theories which aren't complete but hunches mostly xP
So why demons want to posses things and come to Assiah?
First thought that crossed my mind in that they maybe weren't created as bad guys in the beginning, they may have been malevolent but they got the desire for material and Assiah by accidentally first time crossing the veil and possessing somehting. For example you don't know what some thing is before you have tried it (what is cold, how it feels to be sick or hurt). Maybe demons themselves hadn't emotions, but when they got hold of body or thing they got the taste of what feels to be "alive or living" and they got hooked. Now was they want to feel it again and be as lucky as the beings able to be alive, they try to get host through whom they can live through and feel all the glorious things of live.
What kind of place is Gehenna?
Well it could be nothingness and dull place, but I like to think it that there is nothingness but then there is desert and wilderness like in anime scene were Mephisto phones Amaimon who was in Gehenna slaughtering lesser demons. And was in Demon's Etiquette also some backgroud when Rin "flew" off? And if you could somehow enter the place, could you then bring material there? I think that I like the idea of fanfics where Satan lives and rules in a huge castle or appartment, I wouldn't see it a problem to bring things from material world or if Satan indeed has God-like powers he could create thing after he has seen them (going to philoshophy again: you don't know what chair is before you have seen one ---->> demons saw all the wonderful things of Assiah and what humans created from imagination ---->> you can imitate). I really think it would be cool in some point for example to Rin get locked for a while to Gehenna and try to survive there for a while among many, many demons. I want to see the place!
What about Satan possessins Rin? What about breaking his sword?
So does we really have anything proof of Satan wanting to get Rin's body for himself? In anime it is clear but in manga I think there is only a slight reference in chapter 1 and even Satan says so I really don't think he means just to grab Rin to Gehenna and posses him himself, not straight enough said imo. And what Mephisto tells to Rin in chapter 39 is it even possible to possess a demon? Even Rin's heart is locked in Kurikara, I still think he has more close bond with his own body which is perfectly modded for him ('cause he was born with it) so it is even able to exorcise Rin's soul/consciouness or what there is away and to inhabit it? Rin is a half-demon so I don't think vatal verses etc would do the trick. And I think it is quite rare to high class demon like Satan get human offsprings ---->> how to even deal with one so powerfull one? Furthermore, why then Satan let the thing go after chapter 1 - he possibly could order demons to get Rin to him so it has some meaning that he is letting Mephisto raise him and not interfere.
And last point is that if it really comes that it is true that the real reason is Satan wanting Rin's body, I would think it a little dull plot twist. For example many other series have this kind of thing that ultimate evil wants the protagonist's body and Supernatural TV-series are good proof of that. I think Supernatural is known ebough around the world that it would make AnE too much like it, 'cause in the end hunter brothers ended up as vessels...
And what would happen if someone broke Kurikara? I think that it would just set his demon heart free - it is locked in the sword, so I think it isn't really part of it that breaking the sword would harm his heart. It would maybe just return to it's original place, to Rin's body?
And lastly, I really hope the world will stay in two-dimensions. The fresh touch which I really am in love with in AnE is that there isn't angels or heaven that fight against the foul creatures, but humans and other not-so-corrupted things have to take care of themselves. I don't know a series which there would be "Earth and hell but not heaven" so I really wish AnE would stay that refreshing way - third dimension would make me the world maybe a little complicated too :33