I see. So when the cities are big, how do they far being close together?
Well, you have to ask yourself how long the game is going to be and what type of victory. For perspective, hypothetically on a Prince level Pangaea game you could go for conquest or domination with chariots/horse archers and likely finish the game in the BCs are early ADs. There are 24 tiles in a city's BFC of which you probably use no more than 5 or 6 tiles in that whole game if even, you'll be working the strong tiles and whipping units.
Conversely, if going for Space on Prince you are looking at a much longer game, so at some points cities will indeed grow larger after initial whipping phases or later whipping for later wars. With a good performance you are looking at probably a circa 1700AD or later victory (unless you are a master..ha). But even then, you will likely not utilize all of those 24 tiles in a city and keep in mind that specialists are important too. You will use citizens for that as well.
But going back to this game, look at Moscow and St. Pete's. Pete's 1E of Gold is still an excellent city. It has pigs and 1 or 2 exclusive floodplains, and the stone. More than enough for that city for a long time. But it can also share the gold to at times to keep that working early (the bonus commerce from that gold is huge for speeding research or banking gold early on), and it can help grow some cottages for Moscow. So one city whips and the other takes some of the good tiles while that city grows back..
It seems like you should basically just feed your capitol.
Capitals are very important. Like I said - Bureaucracy civic. But I should make one thing clear - not all starting caps are ideal for Bureaucracy. With Bureau caps, you think cottages and for cottages you think riverside grassland or floodplains. Moscow is certainly suited. The Palace can be moved if a more suitable spot presents itself. On Prince this is less important as you may run the map before Bureau really becomes a factor, but it is on higher levels so the concept is worth grasping.
But, to point, well "feeding" is not the right term really. (It is in Civ V with caravans/cargo ships). I term them helper cities. Helping to growing cottages. I've settled less optimal cities nearby the cap in cases just primarily to grow cottages. But I would not call Pete's a helper city as much, even though it can share tiles, because Pete's is a very good city in its on right and will be highly productive for you despite the fact that it can help out Moscow a lot over time.
At what point should I slow down the whipping?
First, I would note that I'm glad that you are starting to use slavery now, but we are a bit blind to how you are using it. Regardless, there really is no definable point to slow down whipping in the sense I think you mean it. It really depends on what you are trying to do. Early on you are going to whip some settlers or workers to expand, or in another case you might whip ..say..some axes for conquest. You also need time to let whip anger wear off. It is a balancing game that you will get a feel for. What you should not do is whip things like warriors or whatever. And don't just whip for the sake of whipping. It is done with purpose.
We can go over this in more detail as we see more of your games.
I will post a link to a post I made some time ago with a few basic primers on whipping - more to understand some timings, mechanics and maximizing whip overflow. It's a link to a post with embedded links to several like discussions I had:
https://forums.civfanatics.com/threads/going-from-noble-tooo.468987/#post-11671673
Also, could someone post a quick explanation of how combat actually works? I know it's logarithmic or whatever, where 2 more strength is far better than 1 more. But anything specific I should know?
1) Except to lose units and don't get overly caught up in the odds
2) Note terrain bonuses and the city defense bonuses (walls, culture) which play into the odds when you attack or when your own units defend.
3) Some units get bonuses on other types of units. For example, chariots destroy Axes on the offense. Spears really like horses. Axes have bonus against other melee units. Some unique units have specific target bonuses like Persian Immortals against Archery units.
4) Early rush is basically about building one unit type en masse based on what strat resource you have immediately available and taking a nearby capital or the AI completely. Chariots are pretty nice on lower levels due to their speed. Axes on the other hand are stronger. (Note what units the AI has available to them though before attacking) ...and note that by early rush we mean very early ..like no more than 1 or 2 cities and access to horses or copper...circa 2500BC to 1500 bc or thereabouts..
5) Later on things like Horse Archers are great or Elephants and Catapults, if access to ivory, or just Axes/Swords/Catapults. But the importance of siege weapons increases significantly as the game progresses, as the AI gets more established and build walls and have better units. (Note: Horse Archers are used in lieu of siege warfare, using their speed instead)
oh..and did I mention BUG mod