How do I remove water deposits from my sink and shower?

Plain old white vinegar - not for all surfaces, or a product called CLR.

the initials for calcium, lime, rust. does a great job on all listed...

You could try CLR or a 50/50 mix of vinegar and dish soap.

Vinegar will remove those mineral deposits. If the shower head also has the deposits, soak a wash cloth in vinegar and wrap it around the shower head and then put a gallon zip-lock bag over it. close the bag as much as you can. Wait at least 24 hours. Repeat if necessary. I have never used CLR but I have heard it also works well.

We had hard water in our old house. Scrubbing Bubbles always worked.

This is what I use:

Heat up 1 cup of white vinegar, mix in about 1/4 cup of Dawn Premium. Not the dollar store kind, because it is too thin. When mixed, pour into a spray bottle and fill with water. Shake. Spray down the grout and let it sit overnight. In the morning rinse. If you have stubborn stains, spray again. Use this mixture a few times a week. It will keep your grout and tiles clean. Also works wonders in the toilet bowl to keep hard water stains at bay. Oh you only have to heat the vinegar one time when you add the Dawn.