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Yes, I think you can overwinter them in your shed as long as it is fairly air-tight and stays above 0 Celsius. Pot them up and let them go dormant; do not water while dormant. Starting late winter/early spring keep an eye on it because it will miraculously send out new shoots. Resume watering and put it where it gets sunlight. The linked article discusses different ways to over-winter them. https://www.gardeningknowhow.com/ornamental/flowers/geranium/how-to-save-geraniums-over-the-winter.htm

I'll assume you are talking about zonal or tender geranium, Pelargonium. There is a whole genus of plants, Geranium, but they are hardy perennials and can be left in the ground. Here is an article that covers how to keep them over winter and start new plants from cuttings. https://hortnews.extension.iastate.edu/2004/9-17-2004/geraniums.html

I believe you are asking about Pelargonium, aka zonal geranium. It is a little late to be taking cuttings but worth a try. You can also dig your plants up and let them go dormant over winter. Usually plants are put in pots and allowed to dry out. Store them at 40 F if you can. Keep an eye on them because "presto chango" they will start to grow in late winter/early spring. At this time you must water it or lose it. Here is a good article, with a video, on taking cuttings: http://www.bbc.co.uk/gardening/basics/techniques/propagation_pelargoniums1.shtml
This article is how to over-winter geraniums indoors: https://www.gardeningknowhow.com/ornamental/flowers/geranium/how-to-save-geraniums-over-the-winter.htm

Not sure, but one guess is it may be from cooler temperatures than the plant would like? I did a quick search for leaf curl or wilt, but your plant's leaves don't look like verticllium wilt or drought. Although Geraniums are not related,I know Rhododendron leaves curl dramatically in cold temperatures. from your photo it looks like just lower leaves are affected. the leaf looks otherwise healthy. Sorry I couldn't be more helpful, but overall, I don't think it's a matter of concern. Will be curious to see how your plant progresses.

Thanks for your gardening question. Experts say that using household bleach can sanitize roots, bulbs and seeds. Chloride is actually considered to be a micronutrient. Although dousing a plant with diluted bleach water is not commonly recommended, what a happy accident for your geraniums! Check out this article:

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/information-on-chloride-and-plant-growth.htm

Happy gardening.