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Yes, you can keep it in the garage. Just make sure to water it about once a month.

This article will help you with pruning: https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/prune-hydrangea-bushes-hydrangea-pruning-instructions.htm

Most likely this is sunscald, which is like sunburn in plants. This typically happens to plants that are in locations that are a bit too sunny for them. If possible, move the plant to a location that is not quite so intense or you can try to shade it some by placing a large umbrella (or something similar) over it. It should correct itself over time as the plant acclimates itself.

Yes, they should work fine on hydrangeas. The powdery mildew can also be treated effectively with neem oil. Here is more information: https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

Hydrangeas are best grown outdoors. If you use one cool white and one warm white bulb in a two bulb fluorescent fixture. You will need to keep the bulbs within 18'' of the top leaves of your plant.

Have they been fertilized and, if so, could you have used too much nitrogen? Usually, when plants don't bloom, fertilizer can be to blame. Too much nitrogen can lead to lush, green growth with little to no blooms. This can normally be offset with the addition of high-phosphorus fertilizer, or bone meal. Here is more information on that: https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/phosphorus-plant-growth.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/bone-meal-fertilizer.htm

This can happen for many reasons, but I would guess that it is due to either a lack of water or it has just reached the end of its blooming cycle. Try soaking the pot (with the plant in it) in a container of water. Sometimes when you water, it might not be going into the center of the soil, leaving the plant too dry.