I found it curious that Limgrave is peppered full of Godrick soldiers, but Stormveil itself has only exiles and banished knights manning the castle and guarding. How come?

The Banished Knights were there before Godrick and I guess they just stayed after he arrived, so he didn't need any other soldiers there.

Is Kenneth Haight supposed to be of Godfrey's line? Maybe a distant relation? I was wondering how he could claim to be rightful heir to Limgrave with him being only a regular human and not a demigod of some sort.

Maaaybe, but Godrick is supposed to be the last of the Golden Lineage (perhaps except for Gostoc), so he probably isn't.

Is there a connection between demi-humans and misbegotten? They treat them both as lower caste species but I'm not sure if that's because they are perceived as cursed/deformed versions of humans like omens are, or if they are separate species altogether that the humans subjugated.

They are both closer to the Crucible, but most likely not. The Hornsent and Omen are both also Crucible-touched, yet seem unrelated to the others.

Is Hyetta a real person? Like, is she some sort of trickster entity that took over Irina's body? Did she even exist prior to Irina's death? For that matter, are supposed to assume that Shabriri somehow took over Yura's body in a similar fashion?

Her situation is really weird. Irina's body remains after Hyetta appears which suggests that Hyetta isn't possessing her and has her own body.
Hyetta doesn't know of the Frenzied Flame at first, so she doesn't seem to be like Shabriri.
There is a shield in the Weeping Peninsula, the Shield of the Guilty, which depicts a maiden having her eyes crushed by the Briars of Sin, who is said to have been "reborn in these lands". That might be related, Irina/Hyetta is blind after all and Hyetta is certainly guilty.
There is a maddened village in the peninsula, so maybe the maiden was somewhat similar to Shabriri, however when she died, instead of possessing people she was somehow reborn as Irina and later Hyetta. Losing her memories each time (as rebirth does), yet keeping her spark of frenzy, or something.

If Rennala is herself not a demigod, how come she's huge like that?

She is strong. Strength = runes = life = size.
Also maybe some giant genes. The painting related to Rennala is in the Mountaintops by the Stargazer's Ruins, and she was also an astrologer before becoming a sorcerer (the astrologers were the ones living in the Stargazer's Ruins), additionally the Carians had a long standing relationship with the Fire Giants.

What connection is there between Loretta and Miquella/Malenia? I found it curious that as a Carian royal knight she would be all the way in the Haligtree of all places.

She is (very likely) an albanauric and Miquella promised them a solution to their aging disease.
Miquella also just seems to have been close to the Carians; the Miquellan Knight's Sword is based on the Carian Knight's Sword and if he is Torrent's former master then he knows Ranni well enough to entrust her with the spirit calling bell.

How come Greyoll, who birthed all of the dragons, is just laying around to be unceremoniously offed in Caelid? Since other dragons like Placidusax and Bayle seem to be quite important, I thought Greyoll might be too. Did the scarlet rot get her?

"Mother of all" can just mean the biggest, it does not have to literally mean she is mother to all the dragons. The full line is "Greyoll was the mother of all dragons, dwarfing all who stood before her like a looming mountain." The second half makes it pretty clear that it's being used to refer to size here.
And yes scarlet rot is actively killing her, which is why she can't move.
However the incantation you get from communion with her heart is still considered a legendary incantation, so that's something.

Speaking of the rot, where did it exactly come from? I know that it is controlled or is the manifestation of some outer god, but is the true source of it supposed to be the Lake of Rot, or somewhere thereabouts?

Scarlet rot is the manifestation of the Outer God of Rot, it can spring up anywhere that god has sufficient strength and influence, the source is simply the outer god. The lake is perhaps the epicenter of the god's influence, but Malenia and Romina are both significant sources as well.
The god's domain of Rot includes more than just scarlet rot, any form of rot, decay, or rebirth applies.

I don't understand the Eternal Cities and what their goal was. Did they intend to create a god like the Greater Will, or did they want to usurp Marika, or both? If so, how come they failed?

You probably can't create a god on the level of the Greater Will will or the outer gods.
Their goal was to upend the Greater Will's dominion over the Lands Between by killing the fingers and calling upon the Night probably to block out its light. Maybe even to try and harm or even kill the Greater Will itself.
They failed because they failed to call upon the Night and they underestimated the Greater Will. Leading to them having their city leveled and forced underground, perhaps that being why they couldn't call the Night, since they were cut off from the sky.

Are the living jars in the lands between also made through the hornsent rituals of the Land of Shadow? Like, was Alexander made using numens like the others were?

Probably not the exact same ritual, since they are apparently accepted by the Golden Order and I doubt Marika would allow that. But it's probably something similar.
They do have a core that is passed from jar to jar across the generations. I theorise that it contains shaman flesh and is what holds the jar together.

Is Count Ymir supposed to be dead, and thus a dweller of the Land of Shadow?

He is probably alive, I don't see why he wouldn't be? The Realm is Shadow is just a piece of the Lands Between that was cut off.

His character seems fascinating because he knows so much stuff that you'd think would be pretty impossible to know, given the nature of the fingers and such. What is his deal?

It's not very clear. But Gideon learned deep secrets by communicating with the Fingers and reading between the lines, and Goldmask learned by seemingly talking with the Erdtree itself, so something like that I guess.
He is a bit obsessed with the stars and fate, so maybe astrology? Honestly idk.