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Rose Of Sharon does not have a terribly long life span.
The long cold winter that nearly the entire United States suffered may also have contributed to the loss of your plant.
I try to remember that a loss in the garden makes for new opportunities.

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

Hand pulling is the recommend and safe way to remove the seedlings from your lawn.

You can prevent further seeding by deadheading the entire spent flower form the plant.

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

Sounds like your Rose of Sharon is putting all of its energy into foliage instead of blooms. Pruning may help force blooms, but not this year.

You can prune the plant in late winter or early spring, while it's dormant.

This article will walk you through exactly how and when to prune your Rose of Sharon:

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

The best time to transplant your plant is when they are dormant. Late fall or spring would be best.

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

Too little water or too much fertilizer are two of the most common causes of "bud drop" or bud rot on the Rose of Sharon. Depending on the zone you're in, this year's temperatures have been particularly high, so try increasing the water (make sure the soil well-drained) and add a light covering of organic mulch.

This article may help you:

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