I work as a Project Manager, although PMP is useful you also need to have previous work experience as a PM and also have a strong technology background (if you are thinking of becoming an IT PM/ or strong business background for Business PM roles..etc)
A combination of education/skills + certification + experience is probably the right mix.
I work around 2 weeks in total remote every month (or better to say 1 week 2 days remote, the second week 3 days remote) managing projects both locally and cross border, it depends largely on the company and how it operates, but i do not know of PM roles that are 100% remote, they probably exist but not the norm i would say.