There is a heated floor in the kitchen, covered with tiles 50/50 cm. Good Italian tiles, not a single crack, lying on the floor for about 20 years. The trouble is that many of the tiles peeled off at its area, while standing firmly in place due to the grout that almost anywhere did not fall off. When you walk on these tiles, there is an unpleasant creaking sound. Since the tiles are good, completely remove and replace all I do not want to.
Are there options to pour under them some kind of liquid adhesive, without removing the tile?
Alternatively, liquid two-component PU glue. It will glue everything together, the layer is minimal, but I'm not sure it will last long.
Another option is liquid nails, but the layer will be thicker, they eventually harden and lose their properties, not the best solution for tiles.
I tend to think you'll have to remove the tiles anyway – it's unlikely you'll be able to pump the adhesive under the tiles properly, and even if you can, the pressure you use to pump will cause the tiles themselves to pop up.
PVA does not work at all, nor does a cement mortar. Neither does PU adhesive.
There are a number of flowable epoxy repair compounds that will even penetrate hairline cracks.
1) Joint filler
2) Cover the edges of the tiles with tape to prevent staining. It is advisable to immediately buy an epoxy remover.
3) Use a syringe with a needle and pump the compound under the fillets and pour it over the joints so that it melts.
4) re-spray the grout.