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Yes, you can grow both hosta and holly plants in Florida but just be sure to provide them with their proper growing requirements--especially some shade.

Yes, it is recommended that you have both male and female hollies in order to produce berries. The following article should be of some help to you:
https://www.gardeningknowhow.com/ornamental/shrubs/holly/how-to-tell-the-difference-between-a-male-and-female-holly-bush.htm

You should not cut away more than 1/3 in any one year. Also, any pruning should be done in winter, though doing so now is ok. This article will help: https://www.gardeningknowhow.com/ornamental/shrubs/holly/trimming-holly-bushes-how-to-prune-holly-bushes.htm

This article will help you with that: https://www.gardeningknowhow.com/ornamental/shrubs/holly/trimming-holly-bushes-how-to-prune-holly-bushes.htm

There are several things that can cause this. One is that it is not getting enough water, either due to under watering or due to a root rot or other damage to the roots.

Where it is planted may also be affecting it. While the other plants are fine, it may be in a spot that gets more wind or more sun, which can also damage it.

And it may also be a fungus. There are several that can cause branches to die off.

I would check the roots for damage and treat with a fungicide. This may help.

There is a pest called a holly berry midge. It gets into the berries of hollies and they will not turn color when they are infested with them. I suspect that this may be your problem. This article will help:
http://www.upenn.edu/paflora/plantclinic/hollyberrymidge.htm

Treating the shrub with neem oil should help with the spiders.