Certified GKH Gardening Expert
Unfortunately, your photos did not come through. I am unable to see the damage.
Flytraps will enjoy a dormancy, though they can survive without one for quite some time. If you prefer to keep them active, then it will only decrease their lifespan by just a little.
With the proper environment and care, these plants will enjoy being indoors, just as they would being outdoors! Here are some articles that will help: