Very briefly (as this is a very large topic):
The production city: Generally the rarest and hardest to find. You'll want a spot with plenty of hills (usually inland and not coastal), but it'll also need several decent food resources (at least 2-3 is optimal) in order to support the population to work all the mines. Keep it basic with the buildings - just a Granary, Forge, Barracks and anything else urgently required (e.g. a Monument for border pop). Aside from this, ignore all research/commerce buildings and concentrate entirely on building military units. Ideally this should become your Heroic Epic / West Point or Iron Works city. Alternatively you could go in the opposite direction if you're more peace orientated, and make this your "wonder central" city.
The research city: The "default" city spot, usually easy to find. Best founded next to a large number of grassland river tiles (or even better, flood plains - though these sites are usually rare). Should have at least 1-2 decent food resources to allow it to grow while working its river cottages, and enough production to produce necessary buildings (i.e. not entirely flatland). Building priorities should be anything that increases research (or commerce) output, such as Libraries and Monasteries. You'll want Oxford University in one of these cities.
The gold city: Can follow a similar plan to the research city, with plenty of river cottages, but simply emphasizing economic buildings (Markets, Grocers, etc) instead of research buildings. The more specialized and unique version of the gold city involves a holy city and religious shrine and/or a corporation HQ or two. The city that has your religious shrine and/or corporation HQ should definitely build economic buildings ASAP, and should also be the city to build Wall Street.
The great person city: Sometimes hard to find, and on some maps an ideal location simply won't exist. You'll want to look for a very large amount of food resources clumped together (ideally 3-4 or more), perhaps with a couple of hills to allow some decent production if whipping too much causes major trouble with unhappiness. Often coastal locations with a lot of seafood are ideal, since working the non-seafood coastal tiles would yield relatively little return compared to the specialists you could hire instead. (I think it's often a shame to have a great person farm inland, due to all the good land tiles that are wasted by not being worked.) As for buildings, you want everything that allows you extra specialist slots - Libraries for Scientists, Markets for Merchants, etc. These can be whipped if necessary, due to the fast growth this city will experience. Later you will want to build the National Epic here, and possibly the Globe Theatre. Moai Statues could also be a good pick if the city has a very large number of coastal tiles.
There are other variations of course, but those are the key ones I recall off the top of my head. For more details, here are two articles I found on a quick search:
City Specialization: Where I do it and
Guide to City Specialization and Land Improvements. They'll explain things in much more detail.
They'd know you cancelled because someone else asked you (they wouldn't care who). The fallout from this would be that the team you cancelled deals with would refuse to trade with you for a number of turns (chosen at random, depending on the leader), as well as thinking more negatively of you (i.e. you get negative diplomatic points from the person you cancelled deals with).
Usually it's not advisable to cancel deals unless you really want to keep a particular AI happy (perhaps they're a very strong neighbour, and you don't want to refuse any of their requests). Also be careful not to cancel deals with anyone who you want to like you.