Tile – Removing calcium carbonate deposits without damaging tiles

Anything is possible, but this falls under the Why On Earth Would You category.

Removing and reinstalling a toilet is a fairly simple job for even a novice DIYer. Don't let that intimidate you into making your project far more difficult than it needs to be.

Without knowing the details, here's a basic outline:

1. Close the water supply valve at the wall.
2. Flush the toilet to (mostly) empty it. Wet/dry vac the remaining water out of both the bowl and the tank (if convenient).
3. Detach the water supply at the underside of the tank. It's likely either a hex nut or a plastic wingnut. Be gentle. This stuff isn't cast iron.
4. Remove the caps for the base mounting bolts (2 or 4), and then remove the nuts.
5. Cut any caulk present against the floor with a utility knife.
6. Wiggle and twist the toilet until it loosens, then carry it out. Optionally detach the tank for easier carrying.

Reinstallation is basically the reverse, but there's the wax ring to deal with. Do a bit of reading here and elsewhere for tips on that.

Try one of the many Grout Restorers or Rejuvenators. They would bring the problem area(s) back to matching the rest of the grout. There are also Grout Coloring Kits that basically paint or stain the grout. You can luck out if a color perfectly matches your grout, but usually you'll have to do the whole floor's grout lines for everything to match. Sealing your grout is the only preventative measure you can take to avoid future situations. This paints on a clear coat & thereby removes grout's porosity. Though, it does need to be re-done every 3 to 10-years...depending on traffic.