How should I fix a previous owners mistakes in this bathroom? (see pictures)
I don't see the mold you're talking about, but my go-to is straight industrial bleach, available at most home centers and hardware stores. I apply it generously (read - dripping wet soaked) with a spray bottle. Give it a couple hours, spray it again.

Repeat until all mold is visually gone.

Get rid of that insulation too. Might be harboring some of the mold spores.

...and, of course, only do it in well-ventilated area, blahblahblah, and so forth....