I've played enough of these games that I have a vague sense of what's going on, but this game has enough small differences in the expansion and economy areas that I'm kind of lost.
First of all, is there a way to permanently toggle a yield display on so when I'm out exploring I actually know if I find a city site or not?
Yes there is a button up on the terrain info window that toggles yields.
Taxation vs. Unrest... I've built several unrest reducing structures but it never seems to effect the unrest number on the tax slider.
The tax slider is showing the unrest taxes cause your empire, the improvements modify unrest for your city. So your city unrest will be different than the unrest in your unrest slider.
When I'm placing a city, what am I looking at for the yields? How many of those tiles factor into a city's production and food growth?
Basically green and purple tiles are what you are looking for. Some resources modify nearby yields so you cna get some nice grain around orchardsa dn nice materials around iron.
Do special tiles like mines and farms have empire-wide effects? If I have 2 mines at one city and 0 mines at another, does building something at the city with no mines still make use of the other ones for bonuses?
No, they effect the city they are attached to.
Some improvements make reference to "per material." What is a material? All the special resources in the game you have tapped?
They are the mittle hammer oyu see in the tile yiel (the other being grain)
What is considered good cash flow vs. unrest? It seems like you start taking too big a hit on production and science to get appreciable cashflow, but unit upgrades, hero equipment and recruiting higher level heroes is very expensive.
Yeap. Dont know an easy answer to this one, what you have described in the intended paradigm.
How do you improve the camps like Troll Lairs, Ophidian doodads and Ogre Mounds? I don't see an unlock in the research tree, though I have been able to randomly build on the Ophidians even though it says I can't, probably due to a bug (they're really strong!!).
Only empire players can build on troll and ogre mounds. That is a bug that you can build on ophidian lairs.
Is there a good reason to spam outposts to keep your territory contiguous, or is it fine to just lock down the key areas and resources you want?
You get bonuses for fighting in your territory, and my ocd wont allow me to not connect my empire together. Outside of that its up to you.