Hello: I can comment on some of this. Softening should be done so it leaves 60 to 120 ppm of hardness in the water. Oversoftening can make anodes work harder and not last long. The other thing it does is to prevent formation of a thin coating of scale inside of copper pipe. You want this coating as it protects the pipe. It’s good practice when new copper is installed to run unsoftened water through it for a few months to let it get this coating. These are suggestions from the National Association of Corrosion Engineers.
So I’d start by making sure the softening is at the right level and then see what the problems are. If the odor is a pain, you can treat temporarily by using hydrogen peroxide.