1. You must have a trade network to their capital. This means both of you having a harbor (with a road from your harbor to your capital, and them having a road from their harbor to their capital). If there is an ocean between you, then you need a certain tech (can't remember which one, Magnetism? Navigation?)to be able trade.
2. You can adjust your expenses in the Domestic Advisor screen (F1), you can move science/entertainment expenses at the top of the screen. Also, on the upper left it shows where your income/expenses are coming from/going to, so you know what areas you can focus on. Building some of the city improvements helps alot.
3. This depends on their feelings towards you (diplomatic relations). Treat them well, by exchanging maps, buy or sell extra luxuries or techs. If you are small and weak, it's hard to gain an alliance with anyone. The best way is to get ahead in techs and sell them techs for gold/turn and/or an alliance against someone else. As soon as someone declares war with me, I will go to ALL the other civs and get them as allies by offering a tech, this prevents my enemy from going to them and getting them as allies first.
Some civs will just naturally be aggressive towards you, it seems no matter what you do, others will be polite or cautious unless you have violated any previous treaties with anyone, in that case everyone will not trust you very well.