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If you bend the branches of your shrub do they break and snap or bend?
If they break off, they are likely dead.
You also can scratch the bark, if you see green underneath, there is likely still life in the plant.
With the long harsh winter that nearly the entire the United States suffered this past winter, and your Michigan location, it would not be an unexpected loss of a plant.
You can prune back the plant and see if you get any growth from the shrub next spring.

https://www.gardeningknowhow.com/ornamental/shrubs/rose-of-sharon/rose-of-sharon-bush.htm

You may have over fertilized. To much Nitrogen in the soil will cause lots of lush green leaves but no flowering.

You could do a soil test to take the guess work out.

Adding Phosphorous with a fertilizer like Bone Meal will boost flowering.

Here is a link to refresh you on care requirements.

https://www.gardeningknowhow.com/ornamental/shrubs/rose-of-sharon/rose-of-sharon-bush.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/bone-meal-fertilizer.htm

After the flowers fade and if they are pollinated they will produce seed pods.
You can pick the pods when they are light brown. Each seed pod will contain 3 to 5 seeds in each lobe of the seed pod.

https://www.gardeningknowhow.com/ornamental/shrubs/rose-of-sharon/rose-of-sharon-bush.htm

Yes, your plant is likely suffering from root rot.

Rose Of Sharon prefer a sunny location with well draining soil.

Perhaps you could move the plant to a new location that would provide these growing conditions.

https://www.gardeningknowhow.com/ornamental/shrubs/rose-of-sharon/rose-of-sharon-bush.htm

There can be a few reasons including environmental, to much or to little water.
Fertilizer issues also can cause this, again to much or to little.
Also Rose Of Sharon can be infected with a fungus call Botrytis and Thrips insects or even a combination of these 2.
A fungicide applied prior to buds forming can help.
Neem Oil is a good treatment since it works as both an insecticide and fungicide. It's safe for people, pets and beneficial bugs.

Here are some links for you.

https://www.gardeningknowhow.com/ornamental/shrubs/rose-of-sharon/rose-of-sharon-bush.htm
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

Yes, you can plant it in fall. Here is more information on its care: https://www.gardeningknowhow.com/ornamental/shrubs/rose-of-sharon/rose-of-sharon-bush.htm