Do bluebells need a lot of sun or can they grow in mostly shade? Are they deer resistant?
Bluebells grow best in part shade-shade and they are not usually bothered by deer. This article should help
https://www.gardeningknowhow.com/ornamental/bulbs/bluebell/virginia-bluebell-flowers.htm
Once the bluebells have finished flowering, can the dead flowers be cut?
Yes, you can cut these dead flowers, or deadhead them, at any time after the flower has died.
https://www.gardeningknowhow.com/ornamental/bulbs/bluebell/grow-wood-hyacinth-bluebells.htm
Should bluebells be cut back after flowering or left to die back?
This will depend on if you want the plant to spread or not.
If you leave them, the flowers can likely go to seed. If they are cut, then they won't spread as fast.
This article will give you more information on the care of these: https://www.gardeningknowhow.com/ornamental/bulbs/bluebell/virginia-bluebell-flowers.htm
My bluebell climber is 3 years old this year the branches have been dying ,I cut the dead ones off but it is still not perked up it has been watered and fed .
Your photos did not come through. I am unable to assess the damage. There are many things that could be affecting the plant!
Here is an article that will give you more information on their care in the meantime:
https://www.gardeningknowhow.com/ornamental/vines/blue-creeper/bluebell-creeper-information.htm
California bluebells (also desert bluebells) can cause a rash if the juice, sap, or hairs of the plant are touched. Bachelor buttons are not toxic at all.
Here are articles that list plants that are toxic for cats: https://www.gardeningknowhow.com/plant-problems/environmental/plants-toxic-to-cats.htm
https://www.aspca.org/pet-care/animal-poison-control/cats-plant-list
https://ucanr.edu/sites/poisonous_safe_plants/Toxic_Plants_by_Scientific_Name_685/