Tile and grout in bathroom can be sealed Gel-Gloss. It cleans and seals the surface as you apply it like car wax. But it does make a surface slippery so avoid using on floors and bottoms of bathtubs. Tile and grout cleaning and whitening article. Tile and grout cleaning and whitening
Other products that work well in the bathtub are C.L.R. or Iron Out. So often the tub comes clean except a haze remains that soaps will not remove. The lime scale removes easily with the proper cleaner. Sometimes white vinegar works well against lime buildup. I like to use it on my windows with T.S.P. because it saves a lot of elbow grease.
For pre-cleaning the tile and bathtub, try Antibacterial Scrubbing Bubbles by S.C. Johnson. The old home-brew of trisodium phosphate (T.S.P.) and bleach works well except the bleach can ruin chrome. Another tip is not to use bleach on rust stains. It can set the stain making removal impossible.