It has been motivated at least in Denmark (limit was 1000, now 100) and Sweden (limit 500) that larger events attract people traveling to it. This traveling and being among large crowds large is what they want to avoid.
While smaller events, say a local low division football team, doesn't normally attract a tone else than locals. The exact number is arbitrary but has to be something, right now 100 in Denmark, 500 in Sweden and will likely change over time.
Yes. The Joe Rogan experience episode with Michael Osterholm talked about this. Basically all of this social distancing is about slowing the spread so as to not overwhelm the healthcare system, not stop it. They can calculate how much you impact the speed of spread if you limit gatherings to 1k, 100, 50, 5, etc. From there it's a somewhat subjective risk assessment of what you want to recommend, bearing in mind that destroying the economy results in deaths from downstream effects.
It’s probably not feasible to come up with anything but an arbitrary number. But 100 allows for important meetings and some ceremonies. More than that are usually public events.
The good thing is that probably you can come up with an educated guess, if you put in a formula, based on that we saw until now how the propagation works. The bad thing is that you will come up with a number much smaller than 100 and it will lead to panic