Weltall

That's actually a really interesting thought. My guess is that it would depend on how long the object had been recycled into some other state from its original one and how different that was from whatever it began as. For example, if you recycled a damaged bottle by melting it down and making a new bottle out of it, there would probably be no real difference. The bottle would still be seen as a bottle by anyone looking at it and the bottle itself would probably still see itself as more or less the same thing. Brandon's mentioned the Ship of Theseus paradox and come down on the side of 'it would be the same ship, Cognitively' so that probably holds for recycling things into very similar things.
On the other hand, recycle that same amount of glass into a decorative paperweight, or divide it up and use it to make the glass portion of spheres and then wait long enough for thinking beings to see the glass as the new paperweight or the multitude of separate glass beads and the Cognitive self would shift accordingly. Then, it might remember that while it's one thing now, it used to be something else and could be easier to Soulcast. It would also depend on what you're trying to Soulcast the object to, versus what it originally was. On that same line of thinking, recycled objects would probably be much easier to Forge.
That said, the Wind's Pleasure gave us an example of Cognitive entities that at one point must have considered themselves separate (ie, all the trees that the wood came from, all the plant fibers in the lines, rigging and sails, the metal in the nails...) now see themselves as a single thing with a very firm Cognitive self-image, so extending that idea to recycled materials there's got to be some point where the recycled thing has gained 'Cognitive permanence' such that it's effectively indistinguishable from the original thing, in terms of Soulcast-ability.

It's more likely that he was hinting at something that was revealed the following year in Arcanum Unbounded, that Devotion and Dominion's power resides in the Cognitive Realm rather than the Spiritual as a result of Odium trying to prevent the power from being taken up again. With all the attendent weirdness on Sel being a result of the powers being both forced together and into a realm where they wouldn't normally be found.

Vorinism teaches that they're different but we don't know whether or not that's true. We know the public teachings of the church at least contradict things we know to be true about the nature of Honor/the Almighty and about the Heralds and what it teaches about the Radiants is suspect per our own observations and Jasnah's in-universe ones, though we certainly don't know the truth ourselves yet. So what the church has to say about the Tranquiline Halls and Damnation shouldn't be taken as an absolute depiction of reality just yet. It's possible Braize is simultaneously both these places, or that Ashyn was the basis for the Halls, or something else entirely.
Now, what the church may or may not know that they don't tell the rest of Roshar is another question. It's possible they're sitting on knowledge they aren't sharing (like the priesthood of the God Kings in Warbreaker or to a lesser extent Mistborn's Steel Ministry) or it could be that they aren't privy to any secrets we'd give an arm and a leg to know and the public teachings are more or less the full extent of their knowledge. Just tossing the potential distinction out there as discussion fuel.
As for the Heralds' prison, both the description in Arcanum Unbounded and Kalak's recollections in WoK suggests they're getting their souls poked and prodded in the Cognitive Realm rather than the Physical. The former because Khriss' description of the planet being populated entirely by 'self-aware Splinters' and the suggestion that some may be Cognitive Shadows points in that direction. Kalak's description of the tortures sounds like the sort of thing that would be much easier to do to the Cognitive aspect of someone than to someone with an actual body that you would need to heal every day. And combining these two streams of knowledge, Kalak recalls burning heat but Khriss claims that Braize is an extremely cold planet, which sounds like it might be an example of Physical/Cognitive inversion like we've seen in Roshar and Scadrial's Cognitive regions where land in one is sea in the other and vice versa.

We know Hoid's relationships with the Vessels came in all types. Leras thought of him as an old friend but was hoping he'd stop meddling in their affairs, something before the Shattering made him have a grudge against Rayse and Bavadin (maybe for independent reasons, maybe linked), he seems to have rather liked Tanavast and he never got along with Cultivation's holder. So for all we know, this one mystery Shard could have been taken up by someone Hoid liked, someone he doesn't think much of one way or the other or someone he hates with a fiery passion because he once stole Hoid's instant noodles.
That said, what Brandon has clarified about the 'Survival Shard' is that it's aware what's going on in the Cosmere and that's why it's keeping its head down and hoping everything will pass it by. Someone with that kind of mindset is highly unlikely to be sending out a multiplanetary team of worldhoppers to do... whatever it is they're doing. We know the Seventeenth Shard has some specific purpose but all we know of that is that one thing they're trying to do is find Hoid. And they have some connection with Frost.

Well, we know that beheading was sufficient to kill Karata because she didn't come back even though she died mere minutes before Raoden 'fixed' the magic so there's no reason to assume an even more thorough destruction of the body would be survivable.
Whether an Elantrian killed by fire is actually dead or not, I don't think we know for sure but I certainly hope it's the former. If beheading is properly death (and there's no evidence that an Elantrian who's lost their head is 'alive but hoed' so I think that's the case) then it's possible there's a Cognitive aspect at work. You think such a thing should kill you no matter what, therefore the Dor can't sustain you. So a burned Elantrian should be dead too under that assumption.

Enough examples of Blades have gone missing that I'm not surprised a lot of Plate is unaccounted for as well. Some could for example have been lost in the early days of the Recreance if people who took up the armor were killed fighting over the shards and didn't understand how to repair it or didn't have access to enough stormlight. Others could be lost as randuir suggests (I mean, if you can lose an entire city under crem... ) or they might have been lost somewhere they couldn't be recovered from even by people who knew where to look. Say, the bottom of an ocean somewhere if there were any naval battles fought involving shardbearers.

Roshar has seasons (sort of) but they're very weird, lasting for a period of weeks and coming randomly. Brandon mentioned in an episode of Writing Excuses (transcript) that they're less what we'd think of as seasons and more temperatue variations interpreted as seasons via translation convention. Roshar apparently has no axial tilt and the combination of that and the semi-unpredicatble highstorms do fun things to the planet's weather patterns.