ok so from what i am hearing, one should use my citys to build settelers and workers.
Mostly, yes. Workers or settlers or artillery units (since they are not affected by barracks, anywhere they are built is fine).
I often find that the AI will leave large gaps between their citys. What should I do about these gaps? Should I:
>not worry about them
>build cheap cultures in captured citys to fill gaps
>settle more citys withing the gaps
>or do somthing els...
The AI plans to use all 21 tiles in a city radius. Foolish AI. In order to make things easy on us, we'll forgo hospitals and let our cities grow to 12 and tweak them for max production. Then they are easier to manage for happiness. Then we can concentrate on smashing the AI.
In the early game, depending on the situation, just ignore them. Plant between them when you want to fight for that new city or really need the resource. In the later game, once your armies get rolling, use those gaps to build a city that will let you attack both cities on the same turn.
another questoin; should you build any improvments in captured citys, the ones that are 90% corrupt?
In the most corrupt, no, don't build any more improvements. Aqueducts and hospitals cannot be sold back; you won't capture any culture buildings, but markets can help remedy unhappy citizens. Barracks are iffy, but most of the rest can be sold. Some Small Wonders (Wall Street, for one) require a number of improvements to be built before that Small Wonder can be built in your civ.
In the lesser corrupt, it depends on how corrupt. If it is producing 6 shields and netting 3, yeah, build a courthouse.
But generally, in the most corrupt cities, don't build anything. Let that city reach it's natural size and make a specialist farm out of it.