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You can try hard pruning the shrubs to revitalize them. I also would clean out the mulch and add new. Here is how to prune shrubs:
https://www.gardeningknowhow.com/ornamental/shrubs/shgen/rejuvenation-pruning-tips.htm

The plant in the photo appears to be a cypress or a juniper, and may get to be very large. It's best if you determine the exact identity of the species and if it is a full size or dwarf variety, and how large it grows.

The salt will affect the nearby shrubs/perennials. Better to use a systemic herbicide cut stump treatment.
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Use herbicide concentrate at full strength (glyphosate active ingredient about 18%) Cut the small tree off down low just above the soil grade and immediately spray or paint the surface of the cut stump with the herbicide solution. It will be absorbed into the root system for a complete kill without affecting the nearby plants.

You can use an ironing type spray bottle, chemical resistant gloves, long sleeve shirt and eye protection to protect yourself. Spray or paint directly on to the cut surface, especially around the outer surface, no need to score or notch the stump. Don't overspray onto the soil or other plants and the environmental contamination will be minimal.

If the branch is still attached, how severe is the break? And where did the break occur, near the trunk or further out. Sometimes if branch end-weight is pruned, a cracked branch will lift up on it's own, close the wound and recover. A professional tree service has capabilities for installation of artificial support systems, cabling and bracing. But with a serious breakage and a hanging hazardous limb, it's best to remove it.
If it's a large tree and large branch breakage, I would recommend having an arborist inspect it and make a recommendation. Keep yourself safe, kids and pets out from under it until you are certain of stability and reduction of risk.
https://www.gardeningknowhow.com/ornamental/trees/tgen/what-to-do-for-storm-damage-trees-repair.htm

Hi. It largely depends on type of shrub and a few environmental factors like time of year and aspect etc. If you would like to explain the situation a bit more i'll shed some light on the subject.
Thanks
Steve

You will want to make sure to look at the tag on the plant for plant height. If the plant does not come with information, then you will have to ask someone working in the garden center to help you to find a plant that will stay within your height range.

Alternatively, you can search for specific shrubs that will be in your height range, and usually come up with quite a few results.

This article will help you to find smaller shrubs: https://www.gardeningknowhow.com/ornamental/shrubs/shgen/choosing-bushes-for-small-spaces.htm