I did my best to settle near food, and yet I still end up with minus 7 or minus 8 when I count the food in my BFCs. It's like I get +2 or +3 from the cows, sheep, or grain, but then everything else is plains.
Sometimes your land just PLAIN sucks (hee hee), but if you have a food resource at least you have the surplus to let the city grow fast after founding. With 10 plains tiles in the BFC it's just natural that it will be a loooong time until that city grows to the limit (probably not before Biology anyway), lots of plains with no food is just not worth settling the spot unless it contains a vital strategic resource.
Oh, and don't plan every city to grow to max size eventually, many games don't last long enough for that to happen anyway, at least not for later cities. For that reason, some city overlap is usually not a problem either.
I also did EXACTLY what you you said about blocking off the Chinese as soon as I could.
Good ;-). It's not easy to overcome the initial habit of settling (more or less) back-to-back starting at your capital, for fear of distance and the enemy filling in "your spots" before you can. On Prince it's still kind of easy to block off land, but the higher you get the harder it becomes. I'm currently trying myself on Emperor where the AI already settles very fast (some of them, at least), so you have to be aggressive as well.
They will be coming out of my stables with 7XP. I will be facing lower level melee and archery units. Maybe I'll see some longbows. All of these cities will be 20% cultural defenses. What promotions are going to make this go most smoothly?
I'm not exactly a warmonger, so take my advice with a grain of salt, but still:
If you go the suicide-horse route then Flanking I and II are the best promotions, because they increase your withdrawal chance. You will probably have to crack single spearmen or pikemen so you kind of need some withdraw% as not to lose too many units to these defenders. I'm not saying that storming in with Knights is not feasible, especially if your opponent doesn't have Engineering yet, but it is often better to go in even earlier (with Horse Archers) or later (with Curassiers and Cavalry) because those units have an innate withdraw% and you get more "bang for the buck" since less casualties on averages means hammers saved for other things.
-- My first thought was one with combat-medic; then the rest with combat-melee and combat-cover. The 10 strength + 10% +25% should be able to deal with most axes and archers, but I thought I'd also have a small chance of withdraw as well.
I recommend building a chariot or horse archer (if either of these is still available) with C1+Medic and then attach your first Great General to that unit
only, giving it an additional 20 XP and opening the Medic III promotion. You then promote with Medic II, Medic III and Morale. You get a 3-movement unit that heals for 25% per turn on its own tile and all adjacent tiles. Many people call this the M*A*S*H unit.
It's good to pick a weak unit for that purpose (e.g. chariot) so it won't "accidentally" defend your stack and die early... Never upgrade it, it will not heal better just from being a Cavalry or Helicopter

. (Well, the heli would make some sense since they have 4 base movement instead of 2, but that would be very late in the game anyway.)
It's totally worth the (high) expenditure of a Great General, believe me.
-- But would it make more sense to go with flanking? Flanking 2 is +10% +20% and immune to first strikes. The first strikes is useless, as the Knights already have that. If I understand it correctly, the +35% from the combat + whatever is better than the 30% withdraw. Please correct me if that isn't true.
+35% from combat promotions does not mean that your chance to win increases by 35%. However, a 30% withdraw chance means that
no matter how strong your opposition is, you always get that chance for your unit to be saved if it had died otherwise. So a high withdraw chance is good if your combat odds are bad, while it won't do much for you if your chance for winning is very high anyway (if they win they won't have to withdraw in the first place).
Therefore, Flanking is good on units that are supposed to "soften up" or "crack through" tough city defenders, or to just generally increase the survival rate amongst your units if your not facing high odds of winning already.
You might not want to give all your mounted units Flanking I+II for the above reasons. Bring some Flanking units to soften the grounds and mop up with Combat units.
-- Then, since these units are starting with 7/10, I should see some level 4 units fairly quickly. What is the third promotion in either line? I could add flanking as the third promotion to the combat line. that would be 10% but would open up the extra 20% for level 5 promotions. That could be really useful after this conflict if I need to upgrade them to cavalry some day.
Sentry is good to have on at least one unit per stack so you can see further. On the Combat line I would probably just go Combat 1, 2, 3, ... and maybe give some counter-promotions (against mounted, melee, archers, gunpowder, ..., depending on the era and units you are facing most likely).
In any case, don't promote your units until they've actually reached their targets, because you might realize that your needs have changed and then you can still decide on a different promotion line than you had originally planned, or distribute them differently etc.
In those games where I've used many mounted units in city raiding campaigns I've gone in with a healthy mix of Flanking II and Combat promoted guys, but I haven't got a lot of experience with this strategy before Cavalry.