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The color to rose of Sharon is variable; you might say unstable. This is especially true of seed that comes from a hybrid plant or one that was cross-pollinated with a different colored rose of Sharon. Hybrids, like cross-pollinated plants have 2 (or more) different parent plants so the seed will have different color genetics, just like our children. To reproduce white flowers, try stem cuttings.

A shrub can die off for many and various reasons.

Winter weather can be an issue, heavy rains or drought. Soil that doesn't drain well can cause root rot. Pests or disease can cause the shrub to decline and die. A shrub also can die for reasons that are never discovered.

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

You can try a rejuvenation prune in the spring.
This article will help you.

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

Many of these blooms will open in succession, or one after another. They won't last very long either. This is the natural process. This article will give you more information on when to prune these: https://www.gardeningknowhow.com/ornamental/shrubs/rose-of-sharon/pruning-rose-of-sharon.htm

Rose of Sharon will do much better outdoors in direct sunlight. Indoor light is a poor substitute for the real thing. Take it out of the tub and examine the roots. They may be rotting if there are no drainage holes. Rose of Sharon is finicky in this way: it likes moist soil but will rot if it is too wet. If the roots look OK, put it in a 6" (or so) container with fresh potting soil and some compost and water well. If you don't have compost, give it a 1/4 dose of fertilizer. Slowly get it used to outdoors giving it more sun each day. It will need special winter protection is you can't plant it in the ground this fall and you live in a climate with cold winter temps. If you are looking for a flowering woody plant for indoors, look into miniature roses.

Flowers will not yield a new plant. If it develops into a seed, you can plant the seed. However, a hybrid rose of sharon will not come true from seed. This is why cuttings are a good idea if you wan't to replicate flower color and size. This time of year isn't the best for cuttings. Take a 4-6" cutting of new growth next spring.