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You've got a regular little mite city going there, don't you. The sticky white egg sacks are probably mealy bugs -- spider mite eggs are too small to see. The tiny spiders chasing the little red dots are just two different sizes of spider mites. At this point, you need to bring out the heavy artillery; don't waste time trying to blast them off with a hose. I'm going to give you an article about getting rid of the pesky little buggers, but whatever you use, be sure to use it 4 times at 7-10 day intervals.
https://www.gardeningknowhow.com/plant-problems/pests/insects/spider-mite-treatment.htm
If you use a commercial miticide, you'll still need to spray for the mealy, as miticide won't touch them. Or you can use a neem oil and/or soap, which will hit them both.
https://www.gardeningknowhow.com/plant-problems/pests/mealybugs-white-residue-on-plants-leaves.htm

Most likely this would be sooty mold. You can control it by following the advice in this article: https://www.gardeningknowhow.com/extension-search/

Start by cutting out the dead branches. I think I would go for a rejuvenation pruning, but the choice is yours. Since you have 3 bushes, you might try a different approach with each one, to see what treatment you like best.

Sounds like you might be talking about a rejuvenation pruning. This article should tell you more: https://www.gardeningknowhow.com/ornamental/shrubs/holly/trimming-holly-bushes-how-to-prune-holly-bushes.htm
If this seems too drastic to use on all the bushes at once, you can prune just a few branches at a time.

Sounds like sooty mold, which you can learn about here: https://www.gardeningknowhow.com/plant-problems/disease/how-to-get-rid-of-sooty-mold.htm
The white strips and brown dot bit sounds like it might be scale insects, which are causing the sooty mold in the first place. When you're treating the sooty mold, you're actually getting rid of the honeydew-producing insects.

They should. This would be a super-drastic form of rejuvenation pruning https://www.gardeningknowhow.com/ornamental/shrubs/shgen/rejuvenation-pruning-tips.htm
but the plant should be able to grow back. BTW, did you get a new landscaper?