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This will depend on the variety of hydrangea that you have. It is most likely a variety that is hardy in your area. Most are hardy from zones 5-9. If this is the case, then keeping them in a garage all winter can do more damage than good, since they will need that cold dormancy to keep them healthy. As for right now, what you will have to do is treat it as a VERY HIGH LIGHT requirement houseplant. Keep in a southern window or under horticultural lights until you can plant it out for the year.

This article will give you more information on their care: https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/growing-hydrangeas-hydrangea-care-guide.htm

Yes, there are sun tolerant hydrangeas but they still need moisture when it is dry and hot. Panicle hydrangeas are the most sun tolerant.

https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/sun-tolerant-hydrangeas.htm

Those are white flies. Here's an article that should help:

https://www.gardeningknowhow.com/plant-problems/pests/insects/control-whiteflies-houseplants.htm

I wouldn't do that, uncomposted. Besides, tomato juice sitting at, only, a pH of 4 will not acidify the soil enough to make a difference. It may also rot, which could be a death sentence to your plant, potentially.

Lemon juice sits at a pH of around 2 or 3, which is much more appropriate to acidify the soil. Just have care to test the pH of your water after adding, so that a gallon remains around 5, or 5.5 in pH. This will ensure that you don't over-do it, or chelate all of the nutrients out of your soil. That would be very counter-productive.

Here are some tips that will help you to achieve bloom color change:

https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/change-hydrangea-color.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/raise-acid-level-soil.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/adding-lime-to-soil.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/lower-acid-soil.htm

Yes, now is an OK time to take cuttings. A stem that did not flower last year may be a good choice. Cut it 5-6 inches long. An article with further info on propagating hydrangeas follows: https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/hydrangea-propagation.htm

'Pink Sunset' is a mophead hydrangea and blooms on old wood (sets bud the season before). Here is more:

https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/mophead-hydrangea-care.htm

https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/prune-hydrangea-bushes-hydrangea-pruning-instructions.htm