What we currently know by observation and threads in the archives of this forum is this:
AI can use any unit to make contact and, unless it has sneak attack plans, it will contact you at roughly the same intervals, I think it was something along the lines of 16 turns.
AI DOES build diplomats and caravans, but teleports them to their destinations, benefiting form quicker and better trade routes (generally the three best trade cities, but enever any of yours, unless you later capture them of course).
Diplomats are rarely used for sabotage or theft, but when it happens it is through an adjacent unit near the city. I've seen diplomats wander around the map, the Chinese once had one out. I suspect they started with writing or at least alphabet, and decided to build their most advanced unit to scout. Or maybe the 2MP were a factor.
AI can bribe your (lone) units through adjacent ones, but I don't know if it uses diplomats for that or the same logic it uses for contacting you - simple proximity of its unit and yours.
AI apparently has a constant pyramids ability, since it always seems to form a new government without a prolonged revolution. In the same turn you get the message, in the diplomacy screen you can already see what they are forming.
AI uses its shield box like a sort of granary. Let's say a city is halfway through building walls - 60 shields, but the AI desperately needs a phalanx. A human would lose 40 shields by switching, while the AI will only SUBTRACT 20 for the phalanx and be left with 40 the next turn.
AI, as mentioned, get wonders for free. I suspect it is also true for spaceship parts, but limited to number of cities per turn.
I've tried to determine if the AI actually spends money when it bribes your units or it rushes spaceship parts, but it's something near impossible to ascertain from within the game. I suspect it's free for them.
I'm surely missing something important, but then there's this thread for that.
