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Heather is very sensitive to moisture levels!
This article will help you.
https://www.gardeningknowhow.com/ornamental/flowers/heather/growing-heather.htm

You can only prune very lightly in early spring. Other than that I do not recommend pruning this. Pruning lightly on an older plant will likely help regenerate it though. Do not take more than a third of the plant at a time. Here is an article that will help: https://www.gardeningknowhow.com/ornamental/groundcover/false-heather/growing-mexican-heather-plants.htm

I cannot find any sources that would state that these have any negative reaction together. Daffodils are common companions for underplanting with roses, but heather doesn't seem to be on any lists. There will be no harm in trying, though. Usually if plants are incompatible, there is copious amounts of information that will state this. This leads me to believe that these will not react to each other in any negative way.

Erica carnea 'Ice Princess' is a common white Heather plant.

https://www.gardeningknowhow.com/ornamental/flowers/heather/growing-heather.htm

You can prune away the dead plant material and see what you have left.
Inspect the plant for signs of pests or disease and treat accordingly.

https://www.gardeningknowhow.com/ornamental/flowers/heather/growing-heather.htm

Do you see bunnies in the neighborhood?

https://www.gardeningknowhow.com/plant-problems/pests/animals/plants-rabbits-dont-like.htm