The tiles on the wall for the bathtub are getting old looking and
some of the grout has black stains, likely from mold. Scrubbing lasts
a week or so before the aged condition reasserts itself. Its a long
time (25 years) since I last put them on and cannot remember the
tricks to the trade. I'd like to do as little work as possible since
there are so much more other "renovation" stuff I have to do too.

First do I need to remove the grout and regrout? Or can I just apply
fresh grout over the old? Only a few spots here and there have lost a
little surface grout of flake thickness. This flake thick loss is not
visible after I clean them.

Can I scrub clean the whole wall and apply some form of polish then a
sealer to restore the tiles? If so what brands should I get? My
water supply is very hard and I think the dullness is from the film of
soap-mineral deposits.