Linoleum over tiles - costs?

Hello everyone,

we want to renovate two living rooms, which currently have tiles (underfloor heating) installed. Instead of tearing out the tiles, we have considered simply gluing linoleum over them.

Question:
1. Is this sensible? Can it be done with underfloor heating?
2. What costs can we expect here per m² (excluding material costs, of course)? The tile joints will certainly need to be filled by a professional, and the linoleum also glued by a professional, since we have no experience with this.
We could only lay laminate, but with underfloor heating I have experienced that the floor often remains quite cool even with impact sound insulation.

Thanks for your opinions!

3. Where can you even get linoleum? In the hardware store I usually only see vinyl/PVC floors. However, we have concerns about plasticizers/health. Or is the PVC available today harmless?