Nice to have limestone for the stove. Absolutely right. Don't you set these with tile adhesive rather than glue? Ideally, the substrate should also be floor gypsum to make it solid.
We have limestone ourselves by the fireplaces. It's actually loosely placed on a cast surface. It's probably way down on the to-do list to fix these with adhesive and grout in between. However, it works quite well loosely too. They lie close together and on an even surface, so they stay in place.