Most of my recommendations about what to do in
beekeeping stem from learning what bees do on their own. We have a responsibility when keeping them to keep them the most similar way to how Nature does it. If you want healthy bees, that is.
I don't normally do splits. I know plenty of people who do and they seem to do well at it, but it doesn't fit my model. I prefer to let them swarm.
I know swarming can be problematic in the
city, but there is a fallback. Be sure you've got desirable bait hives placed around your neighborhood and you'll probably pickup your own swarms when they find and accept your offer of a new home (in the bait box). It's sooo much fun to go out checking your bait boxes and find a swarm happily ensconced in one, already making comb. There is more info on bait boxes in other threads so I'll stick to answering your questions.
Swarms are what Nature tells colonies to do. I rarely find a hive weakened by a swarm leaving. I think that happened to me once and it was with a hive that had 2 or 3 swarm departures which was unusual and not normal. The others thrive once they rebuild their population back up.
You mentioned another reason I like swarming -- because it breaks the pest cycle. Once again, Nature has a solution to a problem, we just have to get out of our heads long
enough to let that work. Same with hive beetles -- on their own a healthy hive can deal with them.
One thing I wish I could convince more people is that letting a weak hive die is perfectly okay. Yes, it's sad for the beekeeper, but this is how Nature weeds out weakness in the gene pool. Don't prop them up; let them die. More healthy bees will be the result of letting the weak bees die off. Be in service to the gene pool and work the way Nature is asking us to.
Florida has its own specific issues, like hive beetles. I'd suggest you keep your bees as healthy as possible with the parts of beekeeping you can control, like healthy organic flowers nearby, good
water (Let a bit of seaweed float in it for the minerals), shade during the heat of summer, letting the colony direct its own mating and activity. Bees are smarter than we humans are on how to best raise bees so I let them do as much of it as possible and mostly try to follow their lead.
warmly
Jacqueline