Alright! Joe is finally being inquisitive. Good questions! UE already gave some good answers, but I will put in my 2cents as well:
A few questions in regard to OF whipping:
*Does the AI use this trick?
AI uses slavery, but not nearly as effectively as the human player. Generally, the main way AI uses slavery is to whip units constantly if you attack them. That is why you see them go from...say...2 Archers in a city to 4 ARchers in like 1 turn..ha
*At what point do you switch away from slavery to a different Labor civic?
This is a good question. Often, I will use slavery for a large portion of the game. AT any point in the game it is extremely effective to get up fast armies if you plan to war.
As UE mentioned, I will use Caste system temporarily in a Golden Age to pump out Great People. If you don't know, Great People production is boosted 100% during a Golden Age. Running caste for those 10 turns or so allows you to run more scientists or whatever in your GP farm or other higher food cities, to pump out as many Great Scientists for bulbing strategies. (The Philosophical trait boost Great People Points as well, as does Parthenon and Pacifism trait in cities that run your religion - if you adopt that religion)
I highly suspect that your use of Great People is lacking in general, so that is something we will indeed address at some point soon.
Later on though, as your cities grow large and you start getting bonuses on improvements like workshops and watermills, you can start to rely more on natural production. At that point, remaining in Caste might be more valuable. Again, it's situational depending on the land and state of your empire, as well as your overall goals.
For instance, if I'm going Space Victory, I generally want to grow my cities large to work cottages, or workshops, and run as many specialists as possible under the Representation civic.
*Is the trick to be as close to 30H, 60H, 90H as possible before whipping?
Yes, if you want to max your OF. For a given #whip you must be less than that threshold. For instance, on a 90H cost item, if you want to 3 pop whip you must be at or less than 29H into the item. If you put 30H into that item it becomes a 2 pop whip - with the least amount of OF. That's simply because a whipped citizen is 30H and as you can see, those are 30H increments.
For settlers, which are 100H cost, the thresholds are 10H (4pop), 40H (3pop), 70H (2pop). So you can't exceed 9H for 4pop, 39H for 3pop (what we just did last night), or 69H for 2pop.
Also, important thing to keep in mind is that you can't whip more than half your citizens in a given city on a give turn. So you need to be at at least size 6 for a 3 pop whip or at least size 4 for a two pop whip. And, yes, at times you can even 4 pop, 5 pop whip or whatever if you have enough citizens and there are times you may want to do that.
Also, keep in mind that certain traits, civics and buildings can alter those whip numbers. For instance, settlers are cheaper with the Imperialistic trait.
In regard to my game:
*What are my immediate goals? I have another settler, but my city location options are diminishing because I'm being crowded out to the west.
*It seems I'm being forced into attacking in order to expand.
Ha...You are not being crowded out at all. One well placed city, and you secure yourself at least 9 or 10 overall cities, which is great early. You could still plan for an early war to take out the Mongols. Maybe with catapults and axes/impis. We can address that later.
This is where I would settle now. It gets Pigs immediately and also will create a seal to the East with Nob's borders, securing your land. It also will be a very nice production city with plenty of food, including lake. Jungle tiles are no concern for a long time...plenty of stuff to work early.
And here's larger view of several cities I dotmap for you:
that sugar/dye/rice city might be a stretch as KK might settle it first, so no fret. You have plenty of cities early on to settle.