LadyWYT

Welcome to the forums! Which version are you playing on? There's been a couple of bugs recently regarding monsters spawning in daylight; one of those bugs was tied to turning off temporal stability, somehow. I don't recall if it's been fixed yet or not, but that's likely what's causing the issue.

What quality were the gems and what quality was the trader after? If the gems you have don't match the quality the trader wants, he won't buy them. My guess is that's what happened here.

They do not drop their horns currently, though they might in a future update.

Welcome to the forums! Sorry to hear about the bad luck with the treasure hunter, but Vintage Story be like that sometimes.
If I understand correctly, your head and leg slots are equipped with iron armor, and the body slot is equipped with leather? That's probably the crux of the issue right there. Iron armor(tier 3) is sufficient for completing the Archive, as the recommended minimum tier is bronze(tier 2). Leather, however, is only tier 1, so most all attacks in the Archive are going to punch right through it. Additionally, your body is more likely to get hit than your legs or head, so if you put your worst armor in this slot it's going to be a bad time. I'd recommend replacing that slot with iron--you should have a much easier time. If resources are a concern, brigandine will be the cheapest option, as it only requires 7 plates and a leather jerkin to create.
Now granted, good equipment isn't necessarily a guarantee of a safe clear, and you don't necessarily need the recommended equipment in order to clear the place. A lot of it hinges on skill and world settings, but for standard skills and settings I would recommend bronze armor minimum, though full iron is ideal.
As far as other tips, I would just bring the ingredients for poultices, and make them as needed. Poultices only stack to 16, but the raw ingredients can stack much higher, so it's more efficient use of inventory. I'd also invest in a lantern, if you have the resources, or otherwise bring an oil lamp. Neither one can be extinguished by water, which is useful in some areas, and the lantern itself will have a much larger light radius than a torch.

I'm guessing it's probably luck of the draw on what size antlers a deer will grow that year. I'm not sure if the size is locked to the individual creature, or randomized per year. In any case, I'd assume it's coded that way so that there's more variety in antler drops, as well as ensuring that the largest horns/antlers are proper trophies.

That's odd...sows should give similar drops to boars. If they aren't dropping anything at all, and assuming you aren't playing with mods that could be affecting the drops, sounds like you've found a bug to report.

Welcome to the forums! What you're seeing here is a snippet of one of the story locations in the game. You can begin the story by talking to a treasure hunter about interesting places.
Of course, if you just want to teleport to the locations without doing the story, I believe the command is /tpstoryloc, followed by the appropriate location name that you would like to teleport to.
Edit: The specific place pictured in this screenshot is...
 

Welcome to the forums! The recipe should be the first two slots occupied by eggs in the cooking, combined with optional vegetables or cheese. However, this is for the vanilla recipe. If you're using the Expanded Foods mod, you'll need to crack the eggs into a bowl first, then add the liquid egg to the cookpot(0.2 L per serving).

Just a side note on temporal stability--as @wildforester mentioned, some chunks are unstable and will cause you to lose stability. Likewise, some chunks are stable and you'll gain stability instead, and some are neutral. The deeper underground you go, the more unstable it gets. Generally, you want to build in a stable chunk, so that you're not losing stability while loafing around your base. Otherwise, you don't really need to worry too much about your stability unless it drops to about 33% remaining; I forget the exact percentages, but that's when the bad stuff starts spawning around you.
To recover stability, the simplest method is to just hang around in a stable chunk for a while. However, you can also sacrifice a temporal gear and a few hitpoints(put the gear in your offhand and use a knife with your main hand) to recover a decent chunk of stability immediately. Likewise, killing monsters will also restore some stability--the tougher the monster, the more stability that gets restored.

Welcome to the forums! There's several to pick from if you search "voice" on the mod DB. Here's a few of them, your mileage may vary:
Id rather meow: https://mods.vintagestory.at/idrathermeow
Meme Scream: https://mods.vintagestory.at/memescream
Celeste Player Voices: https://mods.vintagestory.at/celestevoices
Alternative Seraph Voices: https://mods.vintagestory.at/cobvoices
Shiro's Voice: https://mods.vintagestory.at/shirovoice
Iconic Voices: https://mods.vintagestory.at/iconicvoices

Welcome to the forums! Lightning strike would be my first suspicion. If the option to allow them to start fires is turned on, one could've easily started a forest fire and caused something like this. Aside from that, it could have been a mod thing that a recent mod update might've caused. But I still suspect a lightning strike.

For armor and weapons, it depends on your playstyle. Tier 2 is fine if you're fairly skilled, though iron is perhaps the best choice since it offers more safety for relatively little extra effort to acquire. I do agree with @Zane Mordien, plate isn't the most ideal choice in singleplayer as it will greatly dampen your healing ability and it can be a hassle to try to unequip a piece in the middle of combat in order to heal.
You'll also want plenty of bandages. Honey poultices are the best, but horsetail poultice will do just fine. Bring the raw ingredients and craft a stack or two as needed to make optimal use of your inventory space.
For food, pies are the best, since you can carry multiple slices in one stack. Just make sure to slice the pies before entering the Archive, as you won't be able to slice them inside. Crocks aren't bad either, but crocks do not stack and will take up more inventory slots.
I'd also recommend bringing a trunk or two, depending on how much loot you want to take with you. If you want to take everything that's not nailed down, you'll need to make multiple trips, but the trunks will let you haul everything to the surface for easy retrieval later.
Depends. It's not the same as Minecraft's elytra, but it may just save your life later in the story. If you have access to one, it's not a bad idea to bring it with you while exploring.
Also depends heavily on what you're after. Lore books and fancy clothing items are the main things to find, though there are also several Jonas parts to find as well. If you're after unique knick-knacks, those are more found in chapter two of the story.

Welcome to the forums! It depends on your personal preference, really. If you have the resources for bronze and would rather have more protection when you go out and about, bronze armor is a decent investment. Which style of armor you choose is up to you, though for bronze tier I would recommend lamellar. It's less expensive and easier to make than the other styles, and though the protection might be a bit worse than other styles it'll be enough to get the job done while you work towards iron.
Not necessarily. All you really need to do is find a good ore reading with the prospecting pick, and then dig a shaft straight down until you find what you're after(use the Node Search mode on the propick every so often to make sure you don't miss anything). It's safe to dig straight down in Vintage Story, provided that you're placing ladders as you work. As long as you don't move off the ladder's blockspace(which is difficult to do in a tiny mineshaft), it's impossible to fall off.

Welcome to the forums! Rift activity can last for a while, though the lower values tend to last longer than high activity periods. How often do you check the activity levels? It's possible the activity could have changed, and changed back to Very High without your noticing. Though from what you're reporting here, it also sounds likely that you've encountered a bug. If you've been checking it frequently, and not otherwise messed with any time-altering console commands, I would go report the issue over on the bug tracker.

I think they were added in 1.16, and given how different they are from "regular" trees I wouldn't say they're a precursor to a tree overhaul. It's always possible, I suppose, but not likely.

I seem to recall something being mentioned quite a while back about it potentially getting added to the game at a much later date--closer to the game's completion. I think the reasoning was due to all the possible inventory tweaks that may take place between now and then, that probably break a system like carry-on. So it makes more sense to add that system later, once inventory is really set in stone proper, and not slated for any further changes.
Otherwise, I would guess it could be that the mod no longer fits the intended direction of the game. I can't say that I've played with it, but inventory space is at a premium in the early game, and one of the major challenges you'll need to deal with. Sticking a chest or storage vessel onto your back gives you a looooooot of extra slots to work with, which is a time-saver, yes, but takes a lot of that early challenge away.

Judging by what we have already, I would say most of the horror element is going to be fairly subtle and in the background, aside from certain key scenarios. Temporal storms and the deep underground are two good examples of such scenarios, outside of the story locations themselves. That way players have plenty of time to unwind and enjoy the atmosphere, but still have the occasional reminder that not everything is sunshine and roses in the world.

I generally remove the withered vines. I don't know that it actually does anything, but I presume that by removing them, it frees up space for new vines to grow, and thus increases the chances of getting more pumpkins.

Under the first tab of options when creating a new world, you just need to adjust the Starting Climate to something either warmer or colder, depending on which you wish. Icy will net you the tundra proper, while Cool will give you a taiga instead--similar to temperate forest, but a little more difficult to survive in.
For the tropics, you'll want Hot, but for some seasonal variation without the snow you might opt for a Warm start instead.
Edit: also, welcome to the forums!

Your initial spawn in the world will always be at, or close to 0:0, regardless of starting climate. The Polar-Equator Distance in world settings is what affects how far away the arctic region is from the equator, and thus how quickly the climate zones transition from one to the other. The default value is 100k, meaning that if you start in the arctic you'll need to go about 100k blocks before you hit the equatorial zone.
You just need to head south for the climate to warm up. If you're having to travel further than you'd like to reach the warmer zones, you might consider starting in a warmer climate, or shortening the polar-equator distance when you create a new world.

Shields in Vintage Story are a bit more complicated than in the other block game. You have a passive block chance, which is a chance to block automatically as long as you have the shield equipped. The active block chance is much higher, of course, but requires you to both have the shield equipped and be actively blocking with it by holding the Shift key. I will also note that you need to be facing the general direction of the incoming hit in order to block it, regardless of active or passive blocking.
The better the shield, the higher the chance of a successful block are.

I can't think of anything that you need leather for in order to survive the winter. Larger bags will help you carry more stuff, of course, and better armor will help you fight off stronger enemies. But for just basic survival you don't absolutely need either. I'd say the most important winter supplies are warm fur clothes, plenty of food, and plenty of firewood or peat so you don't need to go gather it should you need to warm up.
For food preservation, I'd cook whatever ingredients are starting to turn stale, and seal the meals into crocks. You'll need fat to seal the crocks if you don't have access to beeswax, which you'll need to go hunting anyway to acquire fat and hides to turn into pelts for fur clothing. Any meat acquired along the way can simply be added to the winter stores.

You should be fine just toughing it out; carrying metal around won't increase your chances of being struck. To my knowledge, the lightning strikes happen randomly, and while it's possible you could get struck by lightning, the chance is very low.

Could just pass it off as those darn temporal storms or a translocator gone awry.
Depends...for the Archive, no that's not normal. As @Thorfinn already mentioned, the Resonance Archive tends to spawn somewhere between 4k and 6k blocks from the world spawn. As for other points of interest though...you might be traveling those kinds of distances in order to get to them.

Teleport yourself to Tobias's Cave via commands, then try the teleporter from his side. It was a little janky when I was messing around with it, but as I recall that got the teleporter link to function correctly.