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This article will help you determine if it is dead:
https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm

For shrubs and trees that are grown for foliage, use a nitrogen rich fertilizer. For shrubs and trees that are grown for flowers, use a phosphorus heavy fertilizer.

It will depend on a lot of things. Mushroom compost is actually cow manure compost, just that it was used to grow mushrooms in. Which is better will depend on the mix that was packaged by the packagers. Look on the bags for the nitrogen amount or the N-P-K. Whichever has the higher numbers is the better one.

This article will help: https://www.gardeningknowhow.com/ornamental/shrubs/loropetalum/loropetalum-shrubs.htm

Some of that turning of foliage is a natural response to the arrival of new growth. A plant will often do this as it prepares to discard the older set of leaves. Other causes are drought or soggy soil, both of which result in root injury followed by yellowing and dropping of older leaves. Fertilizer burn can also damage roots. Finally, as new foliage covers the older growth, it excludes the light to those leaves. In response they can lose their deep purple or burgundy color and in time even turn yellow and drop.

I'm not sure of the symptoms of your shrubs.
They may suffer from Powdery Mildew in moist growing conditions or Scale insects or Spider Mites.
A fungicide for Powdery Mildew treatment and a insecticidal soap if you see Scale or Spider Mites is a good plan of attack.

https://www.gardeningknowhow.com/ornamental/shrubs/loropetalum/loropetalum-shrubs.htm

Several things can cause this, including drought, soggy soil, or fertilizer root burn. However, in many cases it is normal for these plants to turn green as they mature.