I will check out the game later tonight for some detailed micro.
To add to Jastrow's answers:
Why Ikhanda in Bulawayo and not units?
In general you want a barracks in a city before the city starts building units for a war. There are exceptions: if you go for very early wars (with warriors, axes, chariots or even horse archers) where time is of essence sometimes the opportunity cost for a barracks is too high and you may want some more units instead. However, this is not an early war, you already have an established realm. Siege units profit even more so from the starting experience because otherwise they can only level very slowly if ever. Plus you're aggressive, so a barracks in any city that will produce units is really no luxury building.
I wouldn't have known about the OF in Nobamba.
Whenever you're doing some heavy whipping combined with chopping you have to expect to have OF hammers in your cities. This is why it's good to cycle through the builds every turn. A unit can even complete on OF hammers alone while the more costly units get 2-pop whipped or chopped into.
How do you beat the culture defense in cities without a bunch of cats?
As Jastrow said: you can use a spy to set the city in revolt for 1T or simply have a huge stack to beat the defenses. In general you want to have stronger units than the opposition, which is why getting a technological advantage and knowing how to build a stack within a few turns is crucial.
In general, I'm not sure about which civics to use (except slavery) and when. The same with GPs; which should I go for and what is their best use? should I even go for them if I'm going for a conquest win?
Slavery's almost never bad as long as you have food to use it (and as long as you don't forget to use it

) In fact it's not uncommon to spend most of the game in Hereditary Rule and Slavery, while switching away for Golden Ages (say into Caste and Pacifism to get some scientists done). You will get a feel for the civics as you gain more and more game practice. It really is about adjusting your civic choices to your general strategy. And obviously, if you made the effort to build the Pyramids in a game, you don't want to run HR.
I keep asking about my overall strategy because I'm not sure if I just pursue domination/conquest wins. I don't know how and when to plan for Space or diplomatic wins. For instance, looking at this map, what should I be aiming for?
Well, let's look at this map and see how we could achieve various victory conditions:
1. Conquest / Domination: these two are the most trivial victory conditions in the game. There are basically two ways to go about this...
A. Establish a small empire, start warring as soon as you can handle it economically and unit-wise. After conquering an opponent, consolidate and then go for the next guy. This is usually not the fastest approach but it's the safest way to go about it.
B. Play all or nothing: establish a small empire, tech up to a unit that is fast and strong enough to beat the whole map. Stop teching, mass build this unit and beat the map. (This is typically chariots on Noble / Prince, horse archers on Monarch / Emperor and cuirassiers on Immortal / Deity. Alternatively it involves Engineering and trebs.)
This approach requires learning how to tech fast at the start and knowing how to mass-build an army within a few turns, as well as learning how to run a pillage economy and deal with a deficit empire. It's more useful on Pangea-type maps though.
2. Space race: this is one of the victory conditions to fall back to if for some reason you feel conquest / dom would be impractical in your game (say lovefest or vassal relations between the last remaining AIs). To optimize a space win however, you want to start warring early and get a huge and productive empire, which almost trips the domination limit. The bigger, the better. More cities --> faster teching and more production. Even if a city does nothing but build wealth during the whole game. Space optimization usually involves corporations unless the map is very resource poor for a production corporation like Mining Inc. On a resource poor map you might want to go with Caste and State Property instead.
3. Culture: as Lymond already mentioned, this is probably the only victory condition you need to commit to very early. On this particular map a culture win is definitely possible but it would be impractical compared to other VCs. For culture you want multiple early religions (from the AI or self-teched) and you want to establish your future legendary cities very fast.
4. Diplomatic: the other 'fallback victory condition'. It involves either winning a religious victory due to the Apostolic Palace or a United Nations victory.
A. Apostolic Palace: On Pangea-type maps this is the cheesiest way to win a game. Bulb Theology, buld the AP in a religion noone else is running, spread the religion to the AI and get enogh guys to like you (OB bonus, trade bonus, shared war, city gifting, tech gifting, shared religion, favoured civic etc.). Win. There's really not much else to say about it.
B. United Nations: this involves teching up to Mass Media (or alternatively a universally hated AI teching up to it) and building the UN. The diplo machinations stay the same as in A. but you will have more time to build up your relations. It's also a 'fallback' VC tactic if an AI is too strong to tickle militarily.
5. Time: logically this VC depends on score, not finish date. This involves getting an empire that is close to the dom limit (just as with an optimal space game) and getting your population as high as possible (ideally with a food corporation like Sushi or Cereal Mills).
If I played this game on my own, I would still be making a lot of mistakes.
Everyone makes mistakes

The goal is to avoid too many critical ones
Thanks for you help and patience.
You're welcome
