Can every dwarf learn any skill if they try hard enough? Why can't they learn appraisal from zero if they can learn other skills from zero?
They can. Just pick a dwarf and assign them to be the broker. Send them to the Trade Depot by choosing the "trade" option and once they get there and you interact with the menu in any way, they get that skill. So if you start out without one you'll need to wait until a caravan shows up. You can do this trick to get another dwarf the skill if you already have a skilled appraiser by simply temporarily appointing them as broker, sending them to the depot, then unassigning them and putting the usual dwarf back.
What is the purpose of pre-trading conversation? I read that it does not do anything? Is it a bug?
It means you have friendly diplomatic relations with the civilization and one of their diplomats is talking to your own leader. That's why some nobles need offices, and that's where these meetings happen. So make sure the nobles who need offices have them and they're actually accessible. People often just ignore these negotiations and don't do anything with them but they're more useful than you may think. They both ask you to have things they want when they come back, and they offer a better price, or you can request specific things next time they come back, too.
Often their export requests are just dumb and useless and can and should be ignored, they either demand things you're going to keep for yourself or that are so worthless you'd never bother making them. But sometimes they'll want things like shields or bucklers or some kind of weapon you already make a lot of and then you can just churn out a bunch of these things, keep the masterworks for yourself, and sell off the junk, and get a nice price boost for it.
My main requests in the phase where they ask what you want are usually cheap things like unusual ores, but that are ridiculously rare. Cassiterite, bismuthinite, nickel ores, things like that. They're cheap, but you often luck into a map where you don't have any of them, and I really like bronze and bismuth bronze. Later in the game when I'm flush with cash I like buying raw aluminum, rose gold (because it is annoying to smelt bars from other bars), and any of the components of steel if I'm in a map that doesn't have much of it, or I've already gone through my reserves.
The import/export interaction is obscure and it should be more obvious that it's actually useful.
How would I know I need an anvil, pick and axe to survive?
You don't. And it doesn't tell you, although all of these are in the basic embark and you have to deselect them intentionally to end up without them. Also you don't actually need the pick and axe if you bring the material you can make them with. The only strictly necessary item is the anvil, and you can still get lucky and get one in your first trading caravan, if you somehow survive long enough. I think the anvil is the unique game item that can only be created if you already have an anvil. Presumably Armok created the primordial anvil from which all others came, because it is apparently impossible to create an anvil ex nihilo.
Map - am I supposed to settle near something? Does proximity mean I get more/less trade or more/less chance of army marching in? No idea still.
In short, yes. All those guys in the embark menu are the ones who will end up trading with you, attacking you, whatever. Pay attention to those. If you aren't a fan of the undead do not embark near a necromancer's tower for instance. For the first year or so I played I didn't even know you could tab in this menu to look at other aspects of the embark because everything else had kept me so busy.
IMO things like this are the noob killers, or could have been for me, things where some mechanic is actually very important but you could literally be completely unaware of its existence while getting completely thrashed, game after game, because you didn't even know it was there.
Qualities like Critical thinker made me think there's some kind of technology tree exploration thing happening when they are really useless.
Books are expensive but give you nothing. If at least half of the books were "On making mead" and gave a reader dabbling skill it would make more sense to invest in them.
They're getting semi-useful. Also books/slabs can have at least one useful property, they can concern "secrets of life and death" and a dwarf reading them can turn into a necromancer.
Does smelting pollute air? Don't know.
It does nothing. But apparently there is some stress impact from workshops in general and the noise they make, although I have never seen anything in-game that would let you know this or not to just put your living quarters next to a bunch of workshops. But don't do that, although there's absolutely nothing in-game that lets you know that's a bad idea. But so far as I know there is no penalty for disgusting things like fish chop shops and butcher's workshops or whatever other than the miasma.
I want to encrust specific items without spending 40 years setting up a rube goldberg machine for it.
Encrusting is terrible and the ridiculous stockpile mechanics you have to go through, combined with the absolute inability to be specific about it, really needs fixed. I don't think noobs are really dying from not being able to craft absurdly valuable items mainly to boost the value of royal living quarters, but we really should be able to do this fairly simple thing.
Almost all of your suggestions are really things that desperately need to be fixed, though. They're not particularly complex mechanics, they wouldn't be that hard to understand, but the interface buries them under often several layers of obscurity.
As long as I'm even talking about encrusting, though, here's how to do it semi-usefully. Wait until you have Legendaries in whatever you want encrusted as well as the gem-related skills. You can skill them up by working them, having one emigrate to you, or a fortunate strange mood. Build a workshop for the Legendary and restrict it so only he can work there. Don't let it take general orders.
Attach a stockpile to it that only takes items from that one workshop. Assign it to feed the workshop that will actually encrust the gems on it.
Individually assign orders for what you want encrusted.
Similarly, have a jeweler's workshop that is restricted to your preferred jeweler. Also give it a stockpile. You can do another jeweler's workshop to take from that stockpile if for some reason you want the cutter and encruster to be separate dwarves, or for workflow efficiency.
And again, make it refuse general orders and only give it the specific orders for gems you want the specific items to have.
Finally, months later, you can actually produce specific items of furniture (or whatever) and then encrust them with the specific gems you want, after those specific gems have been cut. Finally, you can have that royal bedroom with just a couple items instead of just randomly packing it full of junk for months until it hits the arbitrary royal value, or desperately piling artifact upon artifact in it.