Expenses
The top two things that cost you money in Civ 5 are:
To reduce the first one, be strategic about what you build where. Cities should be focused on a task. Pick terrain, tile improvements, and buildings that compliment this focus. For instance, if you are building a production-focused city, build it near hills and forests, and focus on military and production enhancing buildings. Don't build science or cashflow generating buildings, since you won't be producing much of those in this city.
Likewise, if you are building a science focused city, don't build military or other production enhancing buildings there. The city's focus should be on science or economic enhancing buildings instead.
The only exception is happiness - in order to maintain a positive balance on the happiness scale, you'll likely have to build some happiness generation buildings in most or all of your cities. This tends to be one of the largest trade offs economically in most of my games - do I make the people happier, or do I bank some extra gold?
You can also guide each city's governor to focus on a particular area, and this can help your citizens understand what they need to do in order to support your vision for the city. If you leave the governor alone, the city may ignore some of your tile improvements in order to work tiles that create something you're not interested in, but which makes the city's output more balanced.
Also, don't let your workers run free - focus your tile improvements on whatever works best for the city the tile is in the radius of. Automated workers don't always pick the best terrain improvement for you. They may destroy forest or plant farms around a city that is going to be production focused, for instance.
Every unit you produce costs you money every turn as well. Try to focus your attention towards a small, but mobile army, and don't fight on multiple fronts if you can avoid it. Mixed unit tactics involving ranged artillery units and close-up front line fighters work best. The AI is terrible at war, and they will generally start on the offensive, even though you've likely got your army massed and ready to funnel them into a meat grinder.
If you find yourself with a strong surplus of units, gift some to an allied city-state. You'll gain influence with them, and if you declare war, those units are likely to still benefit you indirectly.
Income
You gain money via citizens assigned to money-generating tiles, trade agreements with other Civs, and by trade routes between cities. Any duplicate of a luxury resource does you no good - it is there to trade.
If you end up with 2 of a luxury, or more of a strategic resource than you need, find someone rich and sell it to them for a tidy profit. Suppling your possible enemies with strategic resources might sound like a bad idea, but since you control the flow of that resource, if they start doing something you don't like, you can cut them off and drastically reduce the effectiveness of any resource-requiring units they produced in the meantime.
There's also a glitch that I don't believe has been patched whereby if you destroy a luxury good improvement (thereby reducing the amount of that luxury good available) you can end a trade agreement early at no penalty, and then rebuild the improvement and sell the good back to that same Civ for another sum of money. This could be considered cheating, and I imagine someday it (will be/has been) patched however.
Roads between cities are generally profitable, but you want to try to minimize the number of redundant road links you have, as having 2 roads between 2 cities counts the same as having one, and costs you extra.
There are many reasons to go to war with another Civ:
- Take their territory and resources - although the game is more balanced towards making small Civs profitable than ever before, in most cases having more territory/cities/resources can still give you a big advantage.
- Halt the progress of another Civ who is doing better than you in some other area - if you have the military, you can stop a Civ who is doing better in technology or culture but who is weak militarily.
- Defending allies or forging new alliances - war is a powerful way to increase your reputation with allied civilizations. Allies can make war against you more difficult, and they'll be more receptive to trade agreements that are beneficial towards you.
- Nip a potential adversary in the bud - the AI in particular is terrible about unit tactics, so you may be able to provoke them to attack you and devote resources to war before they're completely ready.
Depending on why you're going to war, your goals/result will differ. You may wish to simply weaken their army, force them to give you money or other resources, or take a strategic city, but if you're going for a Domination victory, you're going to want to capture or destroy all of their cities, despite their (likely) pleas for peace.
Be wary of growing too large too quickly, as happiness is critical to growth, and extended war and capturing cities leads to rampant unhappiness. If you devote too much of your Civ's resources towards building and maintaining an army, you may fall behind in other areas, giving others room to outpace you.
I tend to prefer to puppet captured cities (instead of razing or annexing them) as this tends to provide a pretty good balance between the benefits of having more territory, resources, and population and the detriment of unhappiness due to size. There may be cities that are just worthless (ie, population 1 or 2 cities in poor positions) and need to be razed, or cities that are extra valuable (ie, high population cities with wonders or other beneficial buildings) that you'll want to keep tighter control over.
Unit tactics have also changed significantly since Civ4 - in that game, you wanted to build large stacks of units to march across enemy territory with at least moderate losses. In Civ5, if you focus on a few powerful front-line defensive units coupled with ranged attacks from siege units, you'll find that your investment in units is small compared to enemy losses. Siege units in border cities can make mincemeat of overzealous enemy armies once war is declared.
Best Answer
I don't think there is any rule that you can follow to build the perfect number of farms, since it really depends on the situation. You can, however, make an informed decision about how many you should build.
To answer your second question first, if a tile is not being worked by a citizen it does not improve your gold, food, or production yield. The only situation where an unworked tile is beneficial is when it contains a luxury or strategic resource. If you aren't working the luxury/strategic resource, but it has the correct tile improvement, it will still be available.
With this in mind, there isn't really a need for 10 farms around a city with 2 citizens. If you listen to the AI recommendations for workers, it will often suggest you build only farms around a low-population city. This is more telling you "you should increase this city's population" rather than "there aren't enough farms." So when building tile improvements make sure you don't just overload on farms. A city with a population of 20 but no production or gold yield isn't nearly as useful as it could be.
In general, try to always consider what improvement would be most effective on a given tile, and what your current goal is. If you have a small city, start by improving tiles that will give you the highest food yield. After you have a few food-generating tiles prepared, try to increase production. This will help you build things such as a water mill or granary in your city itself to further increase growth. After you have a decently sized city you should balance food, gold and production improvements. You want to maintain steady growth, but you also want your city to be as productive and as economically viable as possible.
There is no harm in replacing one tile improvement with another if necessary, but generally you should try to plan ahead by improving tiles in the most optimal manner from the start. City location is very important here, as if you're surrounded by deserts you will always have a weak city.