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Leave any foliage that is still green, since some of it might survive the winter (depending where you are). You can optionally cut off any foliage that dies by itself in the fall.

No, these would not be a plant that would grow indoors with any success.

https://www.gardeningknowhow.com/ornamental/flowers/coral-bells/coral-bells-plant.htm

Curling leaves can indicate pests or even disease.
Check for insects, though some can be difficult to see.
Coral Bells do need well draining soil. If the soil remained too wet and the roots suffered root rot, this could also present itself with dying leaves.

Neem Oil is a good treatment for most pests and even works as a fungicide.

Here are some links to help you.

https://www.gardeningknowhow.com/ornamental/flowers/coral-bells/coral-bells-plant.htm
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

Verify the plants growing conditions with the information in the article below.

https://www.gardeningknowhow.com/ornamental/flowers/coral-bells/coral-bells-plant.htm

You mention that you held back fertilizer this season. If the soil has too much nitrogen, it will inhibit flowering.

You could certainly have the soil tested to determine if this is the cause.

A boost of phosphorous can help get the plants flowering. Bone Meal is a good way to add phosphorous to the soil

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/bone-meal-fertilizer.htm

Coral bells are considered evergreen. Leaves that are ratty and brown may be trimmed but others should remain intact to allow photosynthesis energize the roots for new growth and flowers. I doubt you have killed your plant but may have affected bloom. Be kind to them this spring by watering during dry spells and lightly fertilizing once the weather settles down and you see evidence of new growth.

It would be best to wait until there is no chance of frost, and temperatures remain mild. This can depend on your area and climate zone though. Some heucheras will tend to be more tolerant of the cold, specifically. heucheras.