I'm not sure, but my best guess is that you have your governors managing citizen happiness. When you are a Democracy, you are VERY susceptible to war weariness, and to offset the unhappy population, your city governors are changing laborers to entertainers and your cities aren't producing enough food to sustain the population.
The solution is to:
a) Turn city governors off. They don't know what they are doing.
b) If you are under massive war weariness, revolt from Democracy back to Monarchy (or, if you control lots of land spread out across the globe, Communism might work, too, but I personally don't like it). Monarchy, Despotism, and Communism are immune to war weariness, but Monarchy allows you to rush build improvements with cash rather than by whipping (which becomes more of an advantage the further up the tech tree you climb). You'll lose your trade bonuses, but you also don't have to pay support for a certain number of troops, dependant on how many cities you have and how big they are. You'll probably lose a little of your tech lead (which should be humongous anyhow if you're playing chieftan), but you can continue to happily pursue world domination without having to worry about the home front.
As for the mine question, it's simpler just to explain how the WHOLE production system works:
land improvements like mines, railroads, forests, roads, and irrigation improve the production values of the tiles they lay on. Every city with an expanded cultural border controls 21 tiles in a fat X-shaped pattern (cities with no culture only have 8 squares besides the city square). You can control which tiles get worked by your cities' laborers by zooming to that city (double click on the city, or right click on the city and select "zoom to city"), and click on the tile you want to work. If you mine a square and no laborer is working on that square, than that mine produces NOTHING. You can also use the zoom view to see how many of your citizens are happy, content, or unhappy. If you have more unhappy citizens than happy ones, then your city goes into civil disorder (content citizens don't ccount either way....a city with 8 content citizens and one unhappy one will riot). You can combat unhappiness by:
-Building Temples, Cathedrals, Colosseums, and marketplaces. The first two produce content faces (which turn an unhappy citizen content in the city it's built in), while Marketplaces produce happy faces (which turns a content citizen happy, and works better with more luxuries available), and colosseusm I forget what they do, I hardly ever build them. Some wonders, like J.S. Bach's cathedral, Shakespeare's Theater, and the Hanging Gardens combat unhappiness, too.
-Acquiring luxury resources. The more of these you have, the better they work, assuming you build marketplaces. The AI knows this, too, so they'll likely ask for your firstborn if you try to buy your seventh or eighth luxuries off of them.
-Adjusting the entertainment slider in the domestic advisor's screen. You can use part of your trade income to finance happiness instead of putting it towards scientific research.
-Turning city laborers into specialists. Not the worker units you move around to improve tiles, these are the citizens you see on the zoom view. if you click on a tile being worked, but don't click on another one, it takes that citizen out of production and turns him/her into a specialist. The default is an entertainer, and it produces 1 happy face. You can also turn them into Scientists (1 science beaker) or taxmen (1 trade) if you so desire. Specialists consume two food like other citizens, but they do not create any, so the number of citizens you can use is limited.
Also, you probably learned this already, but relying on colonies to be anything BUT a temporary way to put a resource online while you wait for your borders to expand is a bad idea. Colonies are absorbed by any sort of border expansion and produce no culture border of their own.
So, if your starvation problems are not due to the governors, then I have nfc what it could be. Firaxis really bungled those guys up, but if you want to play on higher difficulties, you should do all of your city management yourself, anyhow. You'll learn things a lot faster that way.
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