You can buy a pumice stone for removing those calcium rings. Had that problem in my upstairs bath where the toilet doesn’t get used very much. Worked like a charm.
Now, for the grout problem. I had a problem in our last house. The tile installer told me to clean the grout with CLR and then use a bleach to kill what’s growing. According to her a small amount of mold will grow, and then the hard water hits that area and leaves a deposit. The deposit kind of seals in the mold.
I have also had great success with my kitchen floor grout using a steam cleaner. Not one of the steam mops, but an actual steam cleaner that shoots out a kind of pressurized steam through a nozzle. I put a scrubber nozzle on and scrub with the steam.
Abrade it away is the only way then. Thanks.