You can use baking soda and hydrogen peroxide for a whole range of cleaning applications, as well as clearing a stopped up toilet.

Mr Plumber has never worked for me clearing a clog. What does work is a wire with a hook on the end for the sinks, and a plunger for the toilet.

Let us know if the peroxide gets rid of the shower gunk. I've tried all kinds of cleaners to no avail.

IIRC the regular hydrogen peroxide didn't do much against those discolorations.

One of the niche magic ingredients to look for is TSP. Alongside bleach (consult proper sources for actual ratios) the combination becomes more powerful against mildews.

I'm reluctant to mix anything with bleach(!)

I'd rather play with sodium hypochlorite than live in a dwelling with mildew.