I'm trying to find any weakness in your points:
1. Dalia wanted Orion to save some item(s) from her inventory (not her inventory) by passing them to Orion (to his inventory). She wanted to visit her favorite Ion server again (with weapons and armor), of course.
2. Because she has a special warehouse for them.
3. Because she had nobody to fight.
[btw, could Annie's swords be the Hyas (the first weapon of Atlas)?]
+ + +
Nova took her Dione from nowhere when they were attacked, so inventory is really 'on a person'.
Why did Thanatos take the Gem from dead Orion? Because it was in his inventory (= on him)
After rebirth Orion should start from scratch, so he can't have any stuff.
= = =
And why Annie and Orion didn't discuss their death on a space station at all?
1. Ion is the server that Annie and Orion went to; we don't even know if Dalia has ever been there. Dalia and Orion were in Ekbar(sp?) the medieval server. Dalia and Orion also go to the roman server. She would Dalia have lost her roman armor if she died to Tahantos in the medieval server? That would seem odd to me.
2. The chick Annie was buying the blade from was an idiot then. If a person full "inventory" is on them and is everything they own, then keeping things in a warehouse they can be stolen from is the stupidest thing anyone could do. If a person inventor is all their item in every server stored as data they can access at any time (as allowed by servers), then there is zero reason not to keep everything you own "on you" and it is more of a risk to keep stuff somewhere else.
3. She had aliens to fight. Just like Nove kills that bear when it sneaks up on her with Dione, if Annie has all her weapons (even if that server doesn't allow her to use her high-level magic) at all times, then she should have taken out her blades (or some other weapon) and her and Orion could have killed all the aliens. One of the reasons the aliens were so dangerous is because no one was armed on the station. Or at least they weren't supposed to be, the Merc guy broke that rule.
Dione is a special case, as a weapon of Atlas it can be used in servers it shouldn't be in. Maat mentions this, Nova shouldn't have had a gun on he while there at all. Also, because it can change shape, she could keep it small, like a single shot Daringer she could carry in her pocket at most times, but then make it change into a sniper rifle or whatever when she needs to. that means that she wasn't pulling to from out of nowhere, like some inventor bag, but she could have had it on her in her pocket the whole time and just pulled it out when she needed it.
Yes, Thantos takes the Gem from Orion because he has it on him, at the time, he had been carrying it with him, remember he didn't even know if it was real at first. But think about the one they stole; it was being kept in a safe but was still owned by that casino owner.
Think about that as well. If the casino owner dies in Eternum, would he really "start from scratch?" Would his bank and hotel and casino in Eternum just go away? Of course not. they would still be his, but any items on him might disappear when his body de-spawns or he is looted. Starting from scratch is just a term, like inventory. The term is somewhat mailable. In nearly every game that has ever been Inventory is the items on the player character at any given moment.
I could be wrong, but I've seen nothing in game that show definitively that a player death makes them lose all their items across all servers, and I think the very existence of vaults, safes, warehouses, banks and such for item storage is a big mark against the idea that a player's inventory is all the items they own and not just the items they carry.