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Most transplanting takes place in spring or fall (preferably fall). If you can ensure that the majority of the roots and surrounding soil is lifted and replanted in similar growing conditions, you'll have a greater chance of success. To reduce shock, trimming may help. Here is an article that you may find helpful: https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm

This article will help you with this: https://www.gardeningknowhow.com/ornamental/shrubs/lilac/lilac-bush-not-blooming.htm

Yes, this is good for lilacs as well.

Lilacs do best when not fertilized. That said, you can use a general-purpose fertilizer (low in nitrogen) in the spring to help give lilacs a little boost. You can also add some compost in and around the soil. If you are having issues with blooming, use a high phosphorus fertilizer or add bone meal to the soil. This article will help with your hibiscus: https://www.gardeningknowhow.com/ornamental/flowers/hibiscus/hibiscus-fertilizing.htm

While in your zone, I would recommend spring planting, you may want to wait another couple weeks just in case another round of winter weather rolls in (unless you properly safeguard them). Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/shrubs/lilac/lilac-care-growing-and-planting-lilac-bush-plants.htm

Well, that doesn't sound too good, BUT it may be possible for the shrub to put out new shoots near the base of the plant, which could be used in creating another should the main plant not survive such a drastic pruning. Unfortunately, you will have to wait it out to see if the lilac begins putting out any new growth at all. If it puts out sucker growth at the base, they can be transplanted and have a good chance of surviving. You need to make sure that they have some roots of their own when you move them. Depending on their size, you may want to pot the little trees up for at least a whole season before planting out in the yard. This way they will be able to form stronger roots.