Welcome to the forum, Tracy!
I’ll get right to the heart of the matter, even though you’re not likely to be happy to hear it. What’s happening is referred to as spalling. As pretty as some material is, not all of it is suitable for a wet environment. And many of the tiles that look like and are sold as “slate” are not suitable for such. I’ve seen a whole lot of “slate” that’s falling apart in a wet shower. Many of the “slates” being sold today are much closer to very hard mud than they are to actual slate. Unfortunately, there isn’t a sealer or a chemical or a process that can stop this from continuing. The permanent fix is to replace the material that’s suitable.
The pictures aren’t clear enough for me to see, but I’m wondering about the shine. Are the tiles on the floor or in the showers shiny?
And the floor tile that’s missing grout is a big red flag that something has gone wrong. This isn’t a normal “wear item” that needs replacing from time to time. Grout should be permanent and last the life of the installation (easily 50+ years). Usually when grout is missing, it’s an indication that the floor is deflecting too much for the stiff grout to tolerate and causes it to very slowly grind onto itself and powder away. In addition, natural stone on the floor has a special minimal requirement to be twice as strong/stiff as that which is needed for man-made ceramic/porcelain tiles. This requirement to have a floor deflection of L/720 is quite unusual (floor that deflects no more than 1 unit of measurement downward for every 720 units of measurement laterally), as it requires pre-planning of the joists before construction of the house to make them strong enough...very few houses have joists this stiff.
I know this is a lot to take in, so please feel free to come back with any questions.
