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It sometimes happens that hybrid plants will 'revert' and display flowers or growth patterns of an ancestor plant, so if you confirm that yours is a single plant, that is probably the reason for the multiple colored flowers.

Two feet is somewhat close spacing for rose of sharon (3-5 feet is recommended), so they probably will end up smaller that they would have been if planted alone. But I don't think they will truly harm each other, they will just be smaller than usual. Making sure they get proper fertilization will help (just make sure to follow the fertilizer label and not to over-apply).

Yes, a Rose of Sharon can grow back from the root stock after it has died down completely.

I would cut down the entire plant this fall and see what spring brings. Add some winter protection with a layer of much around the roots.

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

I would check with the garden center that you purchased from, they often will replace a plant in the first year!

These buds will, more than likely not have time to form before they freeze over. Whether you choose to keep them or cut them is up to you. Here is an article that will help: https://www.gardeningknowhow.com/ornamental/shrubs/rose-of-sharon/rose-of-sharon-bush.htm

This is not an uncommon problem and it could be a number of things from drought, botrytis bud blight, thrips, rot during rainy summers and the shrub running out of energy. Do you fertilize mid-summer? It is too late for fertilizer now as plants are preparing for dormancy and storing energy in the roots. More on the subject here: https://www.purdue.edu/hla/sites/yardandgarden/rose-of-sharon/

Japanese beetles frequently feed on rose of sharon and other plants in the same family. This article may help you
https://www.gardeningknowhow.com/plant-problems/pests/insects/japanese-beetles.htm