Welcome to the forum!
You get inflation mainly from minting (the treasury slider in the budget window isn't completely to the left) and from gold inflation (if you own provinces with gold which make up over 40% of your total income, you get some inflation yearly). Other sources for inflation is for example war taxes and events. You can reduce inflation by promoting mayors to governors with infrastructure level 5. You can also cross your fingers for deflation events.
Inflation increases the cost for everything ingame, also tech costs. Even if inflation is bad for your economy, don't be afraid to mint some. Often it can be worth minting if you get enough ducats to build a manufactory/promote city officials and so on. But try to keep inflation on a reasonable level (e.g. 20%).
I remember when I was new to the game (EU2), I was afraid of running a negative balance in the budget window while treasury was at 0. But you don't need to start minting to avoid an automatic loan; the game will make sure of this, so just have your treasury slider set to the far left (spend your income on infra tech instead, at least early in the game). Of course, if your expenses > your income, you will get a loan no matter what.
Trade in EU2/FTG is very abstract, the resources aren't very meaningful. All settled provinces send their goods to a Center of Trade (COT). You get a share of the values by sending merchants there. Early in the game you won't earn much from it, but later on when you've discovered trade tech 3 (monopolies) and you have access to COTs with low competition, you can make fortunes. You find COTs with low competition mainly in America. Anyway, there's much to say about trading - maybe you can be more specific?
Btw, I recommend the EU2 wiki, it's relevant for FTG:
http://www.paradoxian.org/eu2wiki/index.php/Main_Page