Ooh, these are some fun questions. I may not have the answers, but I kinda wanna speculate a bit, if you don't mind :3 (Obvious *spoiler* warning for anyone reading)
1) The first two I unfortunately have no solid answers for. For Moon's reincarnation cycle, I can't recall if it was ever stated in-game...but the way I see it, it was either the effect of Moon's truest wish given form through Ablaze, or simply a gift from Mother Earth.
It's not really clear how people are born in this universe. Though Zerek said something about sapient beings all being creations of Hers to give nutrients to the world through magic -- lived experiences, expressing their limited individuality for a time, before ultimately returning back to Her when they expire. If She shapes and controls each life in the before and after stages, there's no reason She couldn't imbue a soul with the power to retain its original identity after death.
So if this form of reincarnation is some sort of divine blessing, there's no reason it couldn't happen to others. Granted, all this is assuming She is an active entity, and not just some Law of Nature -- though I'm inclined to believe She is, considering every time a character appears to go underground, we hear a beating heart and are surrounded by red...
If it's the result of Ablaze...I couldn't be sure. So far as we know, there are no limitations to this power other than the caster's own Will. "By the strength of the caster's will, the World surrenders what's needed."
But the embers we've seen derived from Ablaze have never had a duration of more than a few minutes. Even Luke's, with an additional heavy cost, didn't have persisting magical effects (unless you'd count the crystal in Max's spine). So, having the will and desire to craft something with effects decades into the future would require some immensely specific conditions, if such a feat were achievable.
But who knows? Ablaze holds the power to defy fate after all, and our reference points for embers are pitifully few, so it could easily be either explanation (in my opinion. If you see any plotholes, I'd be happy to hear your perspective!!)
2) The same applies: it'd really depend on what controls these cycles to begin with. A nigh infinitely powerful wish, or an omnipotent god?
3) I believe it would be the former. Unless the circumstances required to bring someone back from corruption prevent such a thing from occurring, like it was for Burry's brothers (Though, seeing as they're all attached to his soul, they'll likely go back through the cycle once he dies, either way). Everyone else goes through the same cycle, after all, going off of what Thistle said.
4) We don't know why people forget corrupted individuals, nor what causes corruption to begin with. But seeing through it has everything to do with human mana, and it's power of Truth. (Unless you do what Burry did, I guess, but it's safe to say he's an exception.) My best guess for corruption as a whole is that it's caused by a loss of identity of the soul while in the material plane, completely severing it from Mother Earth as a result.
I'm not sure what could trigger this loss of identity...an unnatural imbalance of others' experiences over one's own, perhaps? (Going off of how Max nearly corrupted when his mana crystal leaked. No idea what's going on with those dark shards, though. (side note: were all of them based on the dagger Alon created? Because I could've sworn Rudy was corrupted before he made it..?))
That would explain why monsters are always made up of multiple different types of mana. And only human Truth could see through all that excess, to the true soul. Hypothetically, at least. As we've seen, there are still special circumstances that must be met to recover someone from corruption. But human mana is always needed.
5) From the Observer's dialogue, it seems his future vision shows him one path that is fixed, which can only be changed through Ablaze, which is why he expresses frustration at Alon's Ablaze, since it diminished the chance at the future he dove into occurring. After which, it shows him a different path, which he can seemingly work to adjust for, based on what happened during Zerek's escape.
Make's me wonder what's weaving the fate he's reading from? Since I doubt he's making it himself.
6) God I hope so!! Alon's route involves our first appearance of the cats in the present; maybe we'll get to see Tharros and Samsun in the flesh! I hope we get to see what they look like at least, whether that's in-game or just in dev posts.
The Cooper route I'd be pretty surprised if we never got, if it's not already a part of new game+ (Alon's route), considering the red paw still has one section missing at "The Call to Honor". (technically two since the 3rd route appears to be missing -- in terms of filling in the red paw, at least -- but I'm chalking that up to a visual error)
And that's ignoring his giant crush on Luke xD
If anything, he seems the most fitting to teach us how to inspire the dogs we encounter on the way to the control tower...but, that "perfect route" could just as easily be Alon's.
...I may have run a little long there....whoops >.>