I'll keep asking more as I find them.
1 Weapons in the store sovereigns can access cost like 10x more than the same weapon when used to outfit a generic troop. What gives? Is there a way to get a weapon on your sovereign for the same low cost a troop can get them for?
2 Mounts in the unit design screen seem to require an actual mount resource. Where can I get these resources? And why can I buy them in the sovereign store as soon as it shows up?
3 Is there any drawback to city spamming? Like, corruption or upkeep costs or something? I have 3 cities right now each with some buildings. I notice something called "admin costs" in the kingdom report screen which seems like it would be tied to empire size or something but that value is at 0.0 right now.
4 Is there any drawback to building crappy L1 buildings in all my cities aside from what they cost? Can I just tear them down and replace them with something good as I start running into the tile limit?
5 How do I enter tactical combat? All my early battles against bears and such autoresolve immediately when I click attack. I never get like a popup box asking me whether I want to micromanage or autoresolve. My sovereign has 1 attack and 0 defense, but his tactical spells can one-shot anything I've encountered so this is kind of a big deal.
6 What do caravans do?
7 How do I increase a city's influence? It actually seems to happen on its own but I have no idea how.
8 How deep into the tech tree do I have to go to start improving prestige?
1: No, the reason weapons and gear cost less for troops is because they also cost materials and time to build, and troops don't level in the same way as heroes do.
2: there are rare resource fields that give you mounts. I have no idea why they show up for you in the store, though.
3: Not as far as I know, but it's better to have well placed cities, rather than a lot of them, as most of your settlement improvements are multipliers that mainly affect your rare resources connected to your settlements.
4: No drawback, but placement of improvements is key: Blocking off a choke, or getting to rare resources. If you REALLY need to, you can demolish them, though.
5: your first battles are usually easily predicted by the AI as a win without casualties. When battles get more risky, you get the choice of tactical battles.
6: Caravans trade with other settlements, which gives you more income. I don't know the system in details, so I can't tell you what way to use caravans is the most efficient. They also create roads between the settlements they trade with.
7: Influence is increased in different ways: When your city grows, in the direction you place improvements and certain improvements (and rare resources) boost these two factors.
8: Entertainment in the civilization tree (Pubs and Inns can be gotten relatively early). And a palace boosts prestige in one city by 7. I haven't found a way to get prestige in settlements without a palace or other special improvements/resources that are limited, above 5.