I had not seen successful AI bribing of my units when I am in Democracy, although I have seen it when I am Monarchy/Republic/Commie/Fundie. The stacking rule is also applicable, although I have "heard" about the AI occasionally breaking that rule. I've even "heard" about the AI bribing away a single city, but I am dubious about that. I'd like to see more documentation of these issues from multiple people.
There is a level, though, of many of the more experienced people not seeing these things because they don't let the AI "keep up with them". Perhaps there is a trigger in the code that permits or disallows this kind of AI behavior, sort of as an "equalizer". My personal way of dealing with the AI is to keep them happy until the end-game, and then to make the end-game as short as possible. I try not to let the AI get into or below "Neutral" attitude toward me, unless it is Bloodlust. In Bloodlust I try to wipe them our or reduce them to caretaker status as quickly and efficiently as possible.
Regarding fast wonder building, are you aware that you can "cash in" a caravan or freight to add 50 shields to a wonder being built? Or that you can start one wonder, then switch to a better one when you get the tech and appear to have finished it in only a few turns? I suspect it may be the latter case, as I do not see the AI using caravans very much. Also, when a wonder has been built, you have the option of not switching a city that was building it for a while, accumulating shields in it until you get the tech for a different wonder. I suspect the AI uses these techniques; what we can do is use the caravan/freight trick to build wonders in <1> turn and not let them get the chance. Rarely does the AI complete a wonder without the warning box coming up "Rome is nearing completion on the Colossus"; a few times I have even had to disband the Phalanx defending the city or a few Temples elsewhere to get the gold to RushBuy the last few shields of a wonder I feel I must have. In general though I shoot for having the caravans already waiting in the city I want the wonder in before I complete the tech.
I have not seen the "co-building" trick, and I would like to see some saves or threads that talk more about it. I would not put it past the designers to do something like that, perhaps reserved for Deity difficulty level, I have just not seen anything on that before. I suspect what we subscribe to these kinds of "tricks" are really the AI using the techniques I described before.
BTW - welcome to CFC! This is the place to ask these kinds of things! If you are asking about "wierd" behavior it helps to have a save or a log of the situation, but just posting the question will sometimes bring others out of the woodwork. The manual does not have all the answers, though it is a pretty decent introduction. This site and Apolyton.Net are good places to "ask the experts"!
