1) It doesnt say it anywhere. They are most likely refering to tiny and small hull sizes. I prefer to think of tiny as a heavy fighter and small as a corvette. You can imagine whatever you wish. The AI names theres small and heavy fighter when refering to the above two hull sizes. I name mine whatever I am feeling like.
2)Economy bases can affect trade routes and planets that fall within an 8 parsec radius of them. How much, if at all, depends on what techs you have researched and how many modules you have added to them.
3) After you research, Republic, Democracy, or Federation the game asks you if you want to change. You can also change it at any time by going to your civilization info screen and going to the government tab. The only reason to switch up is for the bonuses. But if you are an Imperial government you dont have to worry about the voters.
4) The buying options allow you to basically take a loan on the item. The first option allows you to buy the item outright immediately. The three options after that allow you to pay some cash upfront while paying the rest over a number of turns. The number is specified in the terms. If you do the math the loan option is terrible unless you really need it. Like to stay alive. I have used it to successful hold off an enemy.
5) You could be spending money to power your research facilities and factories. I do not know how many you have. Your biggest problem is your moderate pop. In this game pop. = mad cash. You want to have many planets with lots of people. You use the money to "power" your research and construction. You are actually paying for each research point you use and manufacturing point you use. You can go to your economy screen and set your spending slider to influence what percentage you are spending. I really recommend the tutorial for this. You should do them. It will help explain the basics of the economy.
6) Stacked ships are currently troublesome. This is going to be patched this week I believe. The only orders you can give in a stack are to move and to create/disband fleet unless you know the hotkeys. Right now you have to move ships out of the stack to issue them orders. To tell which ship(s) are selected you can look at the list of ships. The ones with a black background behind their picture are not selected.
Hope this helps.