Questions I haven't found answers to yet

#1 Just move on top of said resource in enemy territory.

#2 Civilization got every kind of building, Warfare horses and Fortress buildings, Magic has Conclave Spells and Essence buildings. What you need depends on what you have. There is no right answer for this, though maxing out research first is a good way to get everything  https://forums.elementalgame.com/447952/page/1/ this thread should have more advanced info if you need it.

#3 Bigger map. But eventually those militias will be too slow even though they are high level. Levelups is usually just about more HP, nothing else. I don't bother taking care of the early militias, and let them die quite often, and replace them with leather brethren asap. Then when I got horses/wargs, I start working on my end game army, so they get demoted to city defenders again. I play huge maps, so there usually is enough stuff to level up with, and if it's not, well the AI has plenty of fight to offer ^^

#4 I think there is supposed to be some visual cue, but I never use it. If you remove autoturn it will flash down right when you have spent all movement and all cities have something to do. With autoturn on (default), it should just go to next turn once you are done moving around. 

Thanks.  #1 - that doesn't work for me.  I sit on top of an enemy crystal mine and nothing happens at all.

#5 I see people talking about killing their champions and taking their abilities... how does that work?

Sure it actually is a built mine? You can't destroy it completely if that is what you are after by just moving on top of it. I think you need to have it in your territory to do that. (if so, click on it and select raze, it needs to be unbuilt though, so you need to raze it before taking the outpost etc.)

Steal Spirit. (it's in your spellbook) Only works for magic paths and one or two special spells. So for instance if you get a really bad mage hero, and already have a good one, you can steal their fire magic for your sovereign. (Fire Disciple, so you still need to dedicate 4 levels to max it)

Don't bother too much with trained units' level unless they have a level based trait, because the late weapons and armors are way more powerful than a couple levels; usually lvl1 mages are already better than lvl8 militia. Remember that you can upgrade older units with new armor/weapons, but you can't give them a mount, new accessories (except cloak) or traits; neither the chain/plate armor if they hadn't the right trait at their creation. Sometimes it's more useful to design a brand new unit when certain uprgrades become available. 

Regarding #1, if you move over a resource the enemy has made then you should hear the "Crash" sound and the build here icon should appear over the resource (assuming you have that enabled in options to see the hammer icons). 

At least on the difficulty I play on the AI immediately goes back to build on this tile though - even while having something else in the build queue.  I've ignored a unit sitting on an AI resource for a couple turns and noticed that the shrine or whatever had been rebuild while I sat on top of it, so I just moved off and back on and it was razed again.

I think if you walk over something then walk off, if you go back the immediate next turn it will crash it (raze it) again to be honest.   However, it's not completed that turn just the quequed to be built.

Ok, won my first game really easily. Any one of my armies could have steamrolled all my enemies.

But I still have some questions:

How do I buy scrolls?  They are only available in a town where I've built a specific vendor?

Mounts - I bought a horse for my sovereign with about 5 turns left in the game.  Do they increase the movement of the entire army?

Upgrading troops - holy crap that's expensive.  It looks like it's more viable to just make more troops after I've upgraded my facilities than to upgrade existing ones.  Do you just discard defenders and archers rather than upgrading them?

In regards to you first question #3, don't clear all the lairs... keep some that spawn weak troops (like bandits), they make great harvest for your newly trained upgraded troops to level them up. It becomes a particular art to create XP spawners (basically). I tend to leave darklings, or bandits just outside my borders so I can specifically train my troops up with their wandering mobs.

(I think the comp uses a similar strategy, if not, I'll just spread that rumor to make the computer look that much better).

As to your other questions, I believe your territory is sufficient to be able to open up your shop and I do believe that what you open with your shop in any city is available in any city (Although, I could be wrong here, never thought about the consequence of different areas in the territory. On a side note here, you can also shop in other peoples territory. So you may not have horses, but these other people might, food for thought)

As to mounts, they only increase the movement of the unit that has the mount. So, if you want a movement of 4 on the strategy map then you need all troops to have a movement of 4. But don't disregard mounts in general, on the tactical map that unit with 4 movement will still have 4 movement on that tactical map.

EDIT: Actually I'm certain.  Potions from the Herbalist line are only available in the ZOC of the city that has the building.  I know this because the potion that restores 1 hero wound is only available on the outskirts of the Conclave city that has the Alchemy Lab. 

I'm pretty sure things like Scroll Scribes etc. only allow you to buy their stuff in the city they're in.  (AFAIK, each square in your ZoC is considered to be owned by only one city.)  It might need checking though.

Usually, you don't want to. If the resource is attached to an outpost, you can capture the resource for yourself by simply moving a unit onto the outpost (which captures--not destroys--the outpost and all attached resources). If the resource is attached to a city and you plan on capturing the city, then the same applies. You'll get the resource for yourself when you capture the city.

As far as getting experience for later troops...

If you train all of your units in a developed fortress, they will start a few levels up to begin with. Also, there are usually harder monsters and quests available later for leveling (that were too difficult to take on early in the game).

4) I use the Tab-key to check what units AND cities need orders. Tabbing will hop to the next unit with movemet left and any city that has finished its production (and thereby need a new production order).

No. mounts only improve the sovereign's move points.  So in tactical, your hero will move 4 (or whatever) instead of 2 but in strategic the stack is limited by the slowest lumberer in the group.   If you grab a horse with your sovereign and rally him forth with other mounted units then you can move at max speed.   Add one footsoldier and you are all slowed down again.  capeche?