1: Is there any way of increasing gold cost per city?
There's no "gold cost per city", as such.
There's the gold cost of each building, which you can increase. For instance, maybe you think that the later-era buildings should cost more than 2-3 gpt. So you can edit all of those. In fact, you could use SQL to double the cost of every building, across the board, if you wanted. Or just increase the worst offenders a bit, like making those "+5 happy for 3 gpt" buildings (Theater and Stadium) cost 4 or 5 gold per turn instead.
There's also the trade route income, which comes the closest to being a true cost per city, but it only applies to cities that are connected to your trade network. And yes, you can have negative numbers; before this last patch the equation was (1.0 + 1.25*population + 0*capital). The patch changed it to (-1.0 + 1.1*pop + 0.15*capital), I think. In my own mod it's more like (-2.0 + 1.3*pop + 0.1*capital).
So you could create an effective per-city cost simply by lowering the constant in that equation without adjusting the other factors. However, it wouldn't apply to your capital (although you could give the Palace a gold maintenance cost, to do the same there) and if you made it severe enough, then a human player would just not hook up his cities right away, which'd give a huge advantage over the AI (who isn't that smart).
2: Is there any way of making AI more likely to expand (especially early game)?
A few ways. Lowering the cost of a Settler makes them finish faster, which obviously helps, but raising the Flavor ratings of the Settler makes the AI more likely to build them in the first place. The problem is that the AI is pretty conservative on expansion because of Happiness; he usually won't expand, either through Settlers or warfare, until he has enough spare Happiness to do so without risking dropping below zero. Since the way the AI chooses what to build next is a lot less organized than what a human would do, it needs a bigger "buffer" than a Human would. (The human would, upon building a new city, prioritize happiness buildings in his core cities before expanding if it was going to take him too close to zero. The AI isn't that complex, and won't prioritize the happiness buildings until AFTER he's close to zero.)
There's also an issue with where the Settler is trained. A human who's taken the Liberty tree would know to mainly build Settlers in his capital, where he can get the +50%. The AI doesn't know to do this; all the AI seems to have is a primitive cap, where any build that would take more than ~50 turns is given a much lower priority.
The other issue involved is that the AI often won't scout for good locations, and if it doesn't know of any good sites it won't prioritize the Settler as highly. The AI sends scouts, sure, but it rarely embarks land units to scout an entirely new continent, so all it sees of the New World on a Terra-type map will be its coastline, and that tends to mean it misses out on the inland resource sites.
You can get around this by giving naval units better visibility (and there's a special XML stub in the Technologies table just for naval units looking across land), but it's still an issue, because of one other thing:
When evaluating where to settle, Settlers will generally only check locations within 20 hexes of their current location. (This is set in GlobalDefines. I upped it to 30 in my own mod.) Obviously, on large maps this makes the AI very unlikely to colonize distant locations. There appears now to be an override in place to improve this a bit and allow for some distant island settling, but generally speaking it slows the AI's expansion.