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You can take a sample to your County Extension Office to identify.

https://www.gardeningknowhow.com/extension-search

You can also upload an image and we can help you!

Neem Oil is a great treatment for most sucking pests.

https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

Plants that are in full sun will leaf out earlier than those in partially sunny areas. But no matter where it is planted, one of rose of Sharon's other disadvantages is that it is susceptible to winter injury and twig die-back.
That is not to say that your "unleafy" branches are dead and won't come back; as you noted, they are still flexible. So it is indeed possible that they are even later than the rest of their siblings.

If the plant does not leaf out with more patience, try pruning it down to stress the roots into growing. It you have no new growth, the plant may have been lost.

Rose of Sharon blooms only on wood/stems formed in the current season- often called new wood. Pruning this late will likely reduce the number of blooms this year. In part, it depends on how you pruned it. Giving it a "haircut" by removing the topmost growth (and a lot of new wood) results in a less attractive shrub. To contain height and keep the shrub young and vigorous, remove 1/3 of the branches to the ground in late fall or winter while the plant is dormant. Always remove the largest branches and do this yearly. If the natural size of this Hibiscus is too tall for the space, it is better to remove and replace it with something that meets your criteria.

Two diseases might be at work. One if a fungal leaf spot caused by Cercospora. It starts with spots on leaves that go on to wilt and fall off. The other is a root rot which affects the plant's ability to feed the leaves so wilting and leaf drop are primary symptoms. If you carefully scrape soil from the roots, you may find root galls. Finally there is a blight affecting rose of Sharon, hibiscus chlorotic virus. Take a look of images of this problem to see if that looks like your shrub. Unfortunately, there is no treatment for this virus and the shrub needs to be removed. More info on rose of Sharon diseases here: https://www.hunker.com/13406679/how-to-treat-diseases-on-a-rose-of-sharon-tree

The answer depends on what you consider "good results". You will get maximum blooming in full sun, defined as at least six hours of sun daily. It should still bloom well in 4 hours of direct, full sun. Less than that and you may be disappointed with the number of blooms.

Those are seed pods! If you cut these off, then it will likely flower again. Leaving them on will allow for collecting seeds once they ripen.

Almost all Althea will require the same care, so this article will help with the general care of these: https://www.gardeningknowhow.com/ornamental/shrubs/rose-of-sharon/rose-of-sharon-bush.htm