I’ve had some black mold on the caulk both around my tub and in a small shelf on the shower wall. I got to removing and see that the contractor who did this 3-4 years ago caulked over the grout. I’m going to caulk over the grout along the tub but the shelf was only partially caulked. It doesn’t seem the caulk was needed on the shelf, but I’m not certain. Should I caulk over all grout on the shelf as well as the tub? What is the correct way of doing this?

See the images. I’ve removed old caulk that was along the back bottom wall as well as the bottom sides and half the front bottom. Caulk is down each wall but not horizontal between the tiles. It sure what is needed here. Thanks for any advice.

 

If those pictures are of the grout I see no cracks and it looks really good. Sometimes you see cracks in the corners, just leave them as they are!

 

Wherever there is a change in plane caulk should be used instead of grout. It's not uncommon for those areas to have a little grout under the caulking. To caulk over a fully grouted joint doesn't make a lot of sense.

 

I caulk all inside corner joints. Maybe not necessary but certainly a failsafe.
If you don't, make sure you use the liquid silicone at least twice a year as recommended when finishing a new tiling job.