My friend, no offense, but it looks as though you know almost nothing about this game. Maybe go back to settler level until you can go up to cheiften?
Anyways, for every population point that your city has, that's how many tiles it can work. I recommend farm tiles, especially on flood plains (desert tiles next to a river), or corn\wheat\rice next to a river can all be super effecient ways of gaining food. Cottages won't affect your city if they're not being worked - the same applies for a farm tile. Cottages will upgrade after 10 turns of being worked.
Great people will spawn after your GP meter hits a certain point - then you have a percentage of getting a great merchant, prophet, artist, engineer, or scientists. Prophets help build religious shrines, or can be added to city for +5 gold\turn and 2 hammers\turn, or can be used for a new tech (new techs apply to all). A great merchant can do a merchant expedition in a foreign city that will generate a nice lump sum of money, depending on size and distance from your nation. It can also be added to your city for a +6 gold\turn, +1 food, and I believe +1 science\turn? Artists can be used to add 4000 culture points to a city. If you plan them right, you can 'culture bomb' a foreign city to get it to revolt to your land. you can do this by taking a new settler, making a city near a foreign city (if you want, close as possible) and then use the +4000 culture to kill the other city's land. They'll usually revolt to you unless they have tons of culture. If you add it to your city, it'll create +3 gold\turn and +12 culture\turn. Great engineer's can rush a building (awesome for expensive wonders) by making them instantly come to one turn left or come very close to being completed. They can be added to your city for +3 hammer and +3 beakers. Scientists can create an acadamy that will create +50% beakers and +4 culture I believe. They can be added to the city for +6 beakers and +1 hammer I believe.
The sistene chapel will add +2 culture per specialists, and the representation tech will add +3 beakers for every specialists.
Hills are great for creating hammers (hammers are used for creating buildings and units) and if you chop trees (cut down forests and jungles) the closest city will gain a certain amount of hammers. You need bronze working for forests and iron working for jungles.
By the way, don't use horse archers against spearmen, don't use swordsmen against axemen, and don't use spearmen against axemen. Swordsmen have a natural +10% city attack, making them good against city's, and if you have a barracks (which will give your city's new units +4 xp points, or a free promotion) then you can add the 'city raider' promotion for a +30% city attack, making the unit have 7.8 strength, which makes it -stronger- against axemen in defending citys. Although, if they're fortifying, they're stronger. which they will.
