We have extremely hard water too. The only way that I know to keep hard water spots and deposits from building up on fixtures, sinks, and tile is to WIPE OFF any water that has splashed on these areas immediately after using the water, no exceptions! We have 1” tiles that cover our tub/shower walls. After each shower, we take a towel and completley wipe off all the water from the tile, faucet, spout, everything. As a result, our almost 40 year old tile still looks brand new.
Now I realize, in a public restroom setting, this is never going to happen. But after you get this public restroom back in order, and have gotten rid of all the hard water damage, at least once a week all the tile, fixtures and sinks need to be cleaned thouroghly with something like CLR or Limeaway, to prevent any future hard water deposit build up.
And I still think that the best way to address the current situation is to replace the plumbling fixtures, pipes and fittings and start out fresh. The old ones appear to be very damaged,and beyond salvation. I still think that the tile can be cleaned with an acidic product and an abrasive pad, like a scotch brite green pad, and LOTS of elbow grease. The tile may have some damage underneath the build up of calcium, but it will certainly look a hell of alot better.
Eddie