What's your question? Ask

Sounds like the roots survived the cold, so give it time!

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

Yes, give it more time. Don't prune anything until you have active growth; then you can trim away any dead plant material.

You are outside of their natural growing zone. Even mulching will not be enough to sustain them outdoors through the winter. This will have to be grown as a container species in your area, so that it can be brought in during the colder portions of the year. With this being said, the shrub is probably dead. You can check by cutting back anything that is brittle, until you come to an are that is alive, or green inside. If there is still life, then there is still a chance for survival. If the entire thing is brittle, then it is likely dead.

Weeping branches are this plants natural growing pattern.
These articles will help refresh you on the care and pruning.

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

It sounds like it is getting rootbound in container. You will have to do some root and top pruning to be able to keep it in the same container, or repot it into a larger one. This will correct the issue.

This article will guide you on how to root prune properly: https://www.gardeningknowhow.com/houseplants/hpgen/prune-roots.htm

This can happen with young specimens, as this is how they grow in nature. This is especially true with a variety that is touted for its weeping structure, as this is what allows for the weeping nature. With proper care, it will grow as it should and strengthen up.

This article will help you to care for them: https://www.gardeningknowhow.com/ornamental/shrubs/bottlebrush/growing-bottlebrush-plants.htm