Regarding the economy, Terje439 just started an economic AAR, as you might have seen, that should be helpful, and there are also lots of tips to be found in other parts of the FOF forum. As for your specific questions:
1. As the tooltips indicate, factories produce additional labor each turn and iron works double the amount of iron produced in that city (assuming that you're already set to produce iron there!). You basically have to assess your needs. As the South, you are doing reasonably well in horses but have little iron, so you will want to invest more in getting the few provinces with good amounts of iron (Augusta and Selma, as I recall) to produce even more. The economic system is designed to force the player to make tough decisions -- instead of being able to afford everything you might possibly want, you choose whether to focus more on building artillery (which requires iron and "guns" points) or cavalry (which requires horses), whether your money should pay for diplomacy and blockade-runners to bring in support from foreign powers, or whether your money should be spent instead on building up infrastructure, etc. So, see what you're weakest in and invest early in that. (Playing the South, I usually build a second fleet of runners in the very first turn, so that they can pay for themselves by bringing in more runners goods, and in subsequent turns I start building up my iron infrastructure.)
2. You would alter these city settings if you find that you need more of the other resource. Ideally, you would have each city producing what it is most efficient at producing, but sometimes events dictate that you ramp up production of one type of resource. Basically, look at your stockpiles and try to anticipate your needs.
3. When building artillery you can use the "autojoin" function, or when the unit is finished you select it and move it to the same province as the army/corps/division (ideally using railroad movement for at least part of the way), and once it gets there you add it the usual way. This might take two turns, depending on how far the unit must travel.
I hope this helps. If you have other questions you should post them in the main forum instead of this thread, since people (including me) will see them more quickly.
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