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Slugs are know to eat Impatiens.

Continue to care for the plants and a light application of a balanced fertilizer will help them recover.

Here are some articles with more information.

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

https://www.gardeningknowhow.com/plant-problems/pests/insects/slugs-eating-potted-plants.htm

Yes, they can continue growing, as long as some plant and leaf material is still intact. It's like they were pinched back, which can help produce a bushier plant.

Overwatering displaces oxygen from the soil and can rot the tiny feeder roots. I hope you have drainage holes in the bottom! It also washes away long-acting fertilizer. It is ideal to dig your finger in the soil (or buy an inexpensive moisture tester) to see if the soil is dry. With overhead hanging baskets, I gently push up on the bottom of the pot (or lift, if it is low enough). If it isn't light as a feather, it probably doesn't need water. Once you do this for a few days, you'll get the feel of when water is needed.

This article covers all the reasons impatiens plants might not be blooming. It should help you pinpoint your problem:
https://www.gardeningknowhow.com/ornamental/flowers/impatiens/no-flowers-on-impatiens-plant.htm

There is a serious impatiens threat from what is called impatiens downy mildew, Plasmopara obducens. Other possibilities are nematodes, botrytis blight and verticillium wilt. All of these require removal of the soil to prevent spread to other plants and do not plant impatiens for the next few years. Here are details on impatiens downy mildew: https://www.extension.umn.edu/garden/yard-garden/flowers/managing-impatiens-downy-mildew-in-landscape/
Check you state's extension service for infection status and recommendations for your state.

Impatiens can be cut back. For us northern gardeners, it's a bit late to do this as frost will come in 7 weeks or so. Still, a few weeks of cheerful impatiens is worth the effort. As I recall, there are visible nodes or joints to cut back to and you may already be seeing new leafy growth near the bottom of the leggy stems. Cut back to that. I would fertilize after cutting back and water well.