My garden is not dealing with many pests at the moment, but I still have plenty of small spiders, even in my small apartment yard. You probably have an abundance of gnats, small flies, and/or mosquitos. The spiders that small generally won't affect any larger insects or pollinators, I've seen houseflies rip right through them. I think you may be overfocused on the spiders, they probably just found the best set-up to catch prey.
Aside from that, browning on mangos as pictured can be indicative of nutrient deficiency, salt burn, too much sun exposure, pests, etc. The leaves look healthy but the blooms are dying, which can indicate nutrient deficiency or fungal/bacterial infection, unless Boca has just been experiencing crazy weather recently.
You can consider treating with fungicide and maybe amending soil if browning persists. You can also check the quality of your water source, as salt build-up can certainly take its toll after a few years if not addressed. If you inspect leaves and see a ton of pests, especially scale or aphids, my suggestion would be to get like 3k ladybugs and let them loose at night. I always have better results than with sprays.
Im sure people will have more to add, but thats where I would start. Good luck