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It is best to get rid of all plant materials and soil which have been in contact with powdery mildew and to not compost them. A very hot compost pile could kill powdery mildew fungi, but most compost piles won't get hot enough, so there would still be the risk that the compost would spread powdery mildew to your plants next year.

I hope all is well after that rough storm... I'm sorry to hear about that. Trim off any damaged growth, and let them recover. Here is a link that will help you care for them during this time: https://www.gardeningknowhow.com/ornamental/flowers/impatiens/impatiens-problems.htm

This can be a sign of a few different things. I would ,first, look to a fungal issue. This can cause the wilt. Apply wettable sulfur and dolomitic lime to the soil, then spray the plant with a few drops of one or more of the following mixed with warm water and a spoonful of coconut oil: rosemary oil, garlic oil, lavender oil, neem oil, clove oil, or cinnamon extract.
As for your feeding schedule... I would only feed once a month, at half strength. This could also be causing some wilt, or damage, to over-feed.

This is THE MOST common issue with these flowers. There are two main causes to this.
1. Water stress- These plants must remain moist almost always. They don't require a dry period as much as most plants do. They also do not like being overly-wet either.

2. The other most common issue is heat stress. If the area they got moved to was a significantly different temperature, then this could cause shock.

Here is a link that will give you more information:https://www.gardeningknowhow.com/ornamental/flowers/impatiens/impatiens-problems.htm

It seems that these are just, simply, annuals. You may try to care for them indoors over winter, but they will complete their lifecycle to seed, then die off. The seeds, however, will create the next generation.

Here is an article for more information: https://www.gardeningknowhow.com/ornamental/flowers/impatiens/growing-impatiens-flowers.htm

Yes, you can do this pretty easily. Here is an article that will help you: https://www.gardeningknowhow.com/ornamental/flowers/impatiens/impatiens-rooting.htm