I Want to Know About Eorzean Economics

[Atoli]

There is also trade with other countries/cities/nations/whatever-it-is outside of Eorzea, mainly through the Limsan port. Radz-at-Han comes to mind, for example.
Additionally, "legal" piracy (stealing from Garlean ships) is a nice source of income for the Limsan pirates, and since the stuff is getting sold, there have to be people who trade with these goods.
But like Enkidoh said, most of the general population live as farmers, fishers and hunters.

I also remember that a big reason why Ul'dah strives so well is because of the cheap labour force provided by all the refugees from the catastrophe 5 years ago.
I don't know if arts and crafts are allowed outside of the guilds we know, since all quests that deal with goods created by them (ships, jewelry, haute couture, etc.) always sends you to the respective guild, so there MIGHT be laws in place that forbid the creation of said goods without the supervision of the guild?

We do see a few forbidden goods throughout the course of the story, which of course does not stop people from shipping and selling them anyway. I don't remember the name, but I think some druglike weed is especially harsh to be prosecuted since both Ul'dah and Limsa talk about it in various quests. Trying to find the name right now, I'll add it later.

As for how organisations make their money: donations, mainly. the Crystal Braves for example were mainly financed by the Leveilleur family and Teledji Adeledji (which was it's bane, at some point).
Minfilia's organisation got financial help from the city states, too.
There also IS a tax system in place in each city state, so I imagine that's where the money comes from for organisations like the Barrakudas and other public safety organisations.

Gridania is still a bit late to the whole deal, which makes sense with the whole nature theme going on, but they also have various trading agreements with Ul'dah in place, sell chocobos to the Gold Saucer and agricultural products to, well, pretty much anywhere, but the different mentality of the Gridanian people is often a great hindrance to business as stated by the Lalafell merchant from Ul'dah in the Gridanian market area.