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beorhtwulf
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FYI, Soren from Firaxis has stated that difficulty level has no effect on combat (except for the barbarian bonus).
Re: trading, the AI makes a judgement of the relative benefits of the luxuries to your and its civ when deciding how to trade. If you have a much larger civ (more cities to benefit from the lux), it may want more. Presumably the happiness in its civ is also a factor.
I have heard a rumor that the random-seed calls may have some strange features to prevent the "I lost a combat so I'll load the save game and try again" cheat; you might try not sending series of identical units into the same combat in the same turn. E.g., if you lost an elite cavalry to a regular spearman, try engaging some other enemy elsewhere on the map or something before you send the rest of your cavalry at him. I haven't experimented, so this tip is worth what you paid for it. 
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