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If you have had a hard frost, the plant is probably already in its dormant state. If this is the case, it would be best to move it to a sheltered location (like a garage or near the side of the house) and let it remain in its dormant state. If you store it somewhere that it will not see rain or snow (like the garage), you need to water it once a month.

If it has not frosted where you live, you can still bring it indoors.

It may need more water. Hydrangea like water. If the soil has been allowed to completely dry out (which often happens at the store), it may be repelling water. I would soak the pot in a sink filled with water for an hour or so to make sure the soil is rehydrated, then make sure to keep the plant watered when the top of the soil feels just barely dry to the touch.

If you keep them in pots, you will need to treat them like houseplants. Right now, water only when the soil on top is dry. When the temps rise and you leave them outside all the time, you will find you will need to water them daily. The brown edges on the blossoms are from over watering.

Be sure the container is large enough to accommodate the plant and provides adequate drainage. Its care will be similar to those in the garden, with exception to needing additional water. This article should also help: https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/growing-hydrangeas-hydrangea-care-guide.htm

Yes, it can be transplanted, but I would put it off until fall if at all possible. However, as long as the plant is properly acclimated beforehand and the temps are not too hot/cold, you can still go ahead and put your hydrangea in the ground now. In other words, if hydrangeas are hardy in your area, they may be planted in the spring after all chance of frost is gone and preferably before the hot conditions of summer arrive. They must also be conditioned to the outdoors gradually. Be sure to place it in a suitable location and give it plenty of water deeply until the plant establishes itself.

These articles should help: https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/growing-hydrangeas-hydrangea-care-guide.htm
https://www.gardeningknowhow.com/houseplants/hpgen/acclimating-houseplants-outdoors.htm
https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm

It could be either black spot or sooty mold. Both are treatable and in most cases, not fatal to the plants. These articles will help:
(this is about black spot on roses, but it applies to all plants) https://www.gardeningknowhow.com/ornamental/flowers/roses/black-spot-roses.htm
https://www.gardeningknowhow.com/plant-problems/disease/how-to-get-rid-of-sooty-mold.htm