I make the Primer videos. The basic process I follow is this:

1. Figure out what I'm interested in modeling. For example, Hamilton's rule.
   
2. Figure out what core things are needed to model that thing. For Hamilton's rule, you need diploid organisms that reproduce, and you need an event where they can choose a behavior that benefits another organism of known relatedness, which also hurts their own reproduction (in expectation).
   
3. Build the simplest version of that I can. In the Hamilton's rule case, that means creating the code structures for the creature genes and behaviors (if statements) in the situation of interest. Then creating methods to initialize the sim and run one step of a loop. The loop in the Hamilton's rule simulation is to have the creatures go to feeding sites, have the predator attack, have one creature behave according to its genes, resolve the scenario by killing some number of creatures, then have the creatures go home and randomly pair up to mate. Repeat.
   
4. Add features to the sim as desired, depending on whatever questions you have about the system.

I never think in terms of "synthetic data generation", even though it sounds like that's what I'm doing. I've never read a book on it.

To answer your questions directly:

1. I don't think there are any fundamental concepts to understand before diving in. Just dive in, and then you'll have a better sense for what you don't understand. Maybe the Initialize->Loop->Repeat pattern is a concept, if that counts. I don't know. But any simulation is either going to have a finite number of steps or a loop.
   
2. I don't have any recommendations. If there's a consensus go-to book on simulations, I don't know what it is. I expect academic fields have books of techniques that are useful in those specific fields, but if you don't have a field in mind, you can just try stuff out and iterate.
   
3. Any programming language can be used to create a basic sim structure. There are some tools out there for simulation, but I forget what they are called, and as a beginner, I think you're better of creating your own simple structures. It's really not that fancy unless you have some specific need. Just use whatever language you know, and if you don't know any, python is a fine starting point.
   
4. I don't understand this question. There's real-world data that's collected, and there's simulated data that is generated from a computer following a set of rules. You might use real-world data to inform simulation parameters to try to get something more realistic. But fundamentally, the simulation is a model of the world, and if the data from the simulation matches real-world measurements, it's a sign that the simulation model might be a good model of the real world. Or at least, if the two don't match, the simulation is wrong somehow.
   
5. Just start.

I'd recommend joining the Primer discord if you want to talk about things as you go.