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This is most likely due to an insect issue. There are many that I suspect that it could be, unfortunately. This collection of articles will give you more information on making your own pesticides, fungicides, and other helpful information: https://www.gardeningknowhow.com/special/organic/

Yes, this is a good way to control its height. This article will give you more information: https://www.gardeningknowhow.com/ornamental/shrubs/bottlebrush/pruning-bottlebrush-plants.htm

Bend the tips of the branches, and if they are brittle, then cut them until you see green, or they get bendable without snapping. Prune down to this point, and they should be fine. There is not really much that you can do, until you see if it is alive or not.

Yes, I would wait to do any pruning or clean up until after it blooms.
Here are some articles with more information.

https://www.gardeningknowhow.com/ornamental/shrubs/bottlebrush/growing-bottlebrush-plants.htm
https://www.gardeningknowhow.com/ornamental/shrubs/bottlebrush/pruning-bottlebrush-plants.htm

You are in zone 7b.
Most Bottlebrush are rated zone 8b-11.

I did a bit more research and and I found an Alpine Bottlebrush and Woodland Red are listed as hardy down to zone 7.

Do a Google search for growers or check your local garden centers.

https://www.gardeningknowhow.com/ornamental/shrubs/bottlebrush/growing-bottlebrush-plants.htm

This can be due to several reasons. If the area remains too wet, or too dry it can cause this. Can you include a photo, and your growing zone? This can help me to make a better diagnosis.