What's your question? Ask

Burning bush is very forgiving of severe pruning. Try cutting it down to 12 inches before new leaves emerge. Another strategy is to remove 1/3 of the oldest, widest branches each year. This classic method avoids the jarring eye catcher of a large shrub cut down to a stump. In 3 years you have a shrub of a more compact size. Since it is such a vigorous grower, continuing to remove the largest branches annually rather than clipping the top growth to contain size yields a more attractive shrub with more leaves. It also creates openings for sunlight which is necessary to keep the center from losing its leaves. Older wood is, well, woodier; younger branches have more leaves. The choice is yours.

What you are relying on is the plant's roots. Unless there are new foliage/stems emerging, you don't need to cover the stooled shrub.

You can do this. It will not harm anything at all.

These have a lifespan of, roughly, 250 years. There is likely something wrong with the soil. It would be very hard to know without photos, and detailed information on their care, though.

If you would like a detailed description of your problem, it will be best to get your soil sampled.

Your local extension service can help. This link will help you to find the closest to you: https://www.gardeningknowhow.com/extension-search

It will be hard to say without a photo, but it could very well be a fungal infection.

It is a good idea to trim off any growth that is completely dead, or brown, and treat the soil with a HANDFUL of DOLOMITIC LIME and a TABLESPOON of WETTABLE SULFUR per plant. This will condition the soil, and prevent infections during wet seasons.

in the meantime, this article will help you to care for these shrubs: https://www.gardeningknowhow.com/ornamental/shrubs/burning-bush/burning-bush-care.htm

At some point everyone needs to make the harsh decision to hard prune their Burning Bush.
You can certainly trim out any dead plant material now and then do more pruning later or early spring.
This article will help you.
https://www.gardeningknowhow.com/ornamental/shrubs/burning-bush/pruning-burning-bush.htm