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Probably not well. These plants prefer full sun but can tolerate partial shade.

Hard to say for sure but it sounds fairly positive that your hibiscus is putting out new growth. You may want to trim any old or unhealthy branches and keep a check on the soil moisture so the plant doesn't get too dry (or too wet, which is just as bad).

The white insects that you mention could be whiteflies. As for the worms, are they green? If so, they can usually be picked off or treated with products containing Bacillus thuringiensis (Bt), which is a natural pest control targeted at caterpillars and worm-like insects. Here is an article that you may find helpful as well: https://www.gardeningknowhow.com/plant-problems/pests/insects/whitefly-control.htm

It sounds like you may have thrips. These articles will help:
https://www.gardeningknowhow.com/ornamental/flowers/hibiscus/hibiscus-flowers-hibiscus-blossoms-falling-off-plant.htm
https://www.gardeningknowhow.com/plant-problems/pests/insects/controlling-thrips.htm

It is best to leave any pruning till spring, as the foliage helps with additional protection in winter. This type is generally winter hardy in Zones 5-10 but colder regions will require additional protection or overwintering indoors.

If they are hardy hibiscus, you do not need to do anything. They tolerate winter very well to Zone 5 without help. If they are tropical hibiscus, they will not be able to survive in the ground over the winter outside of Zone 9 or higher. These plants will not tolerate more than a night or two of light freezes. Even one hard freeze (below 25) could kill the plant. You will need to dig them up, place them in pots and bring them indoors for the winter.