Flooring. Laminate, engineered parquet, vinyl? Where is the best place to buy?

Minor unevenness in floating installation is not a problem. Full vinyl glued down does not tolerate it.

There is also impact sound insulation underneath, right?

Yes, it is already integrated.

in the children's room it gets scratched anyway

I say quite clearly: no. We have had solid wood floorboards in the children's room for 3 years, there are small marks in them, but every floor gets such marks over time. Personally, I would think twice about simply laying the floor on top of underfloor heating. In my opinion, for reasonably good heat conduction, the floor should be glued down (especially if the heating only has a low temperature anyway).

We have also glued parquet in all rooms. Only the hallway on the ground floor, kitchen, and bathrooms have tiles. Otherwise, there is parquet everywhere. After 1.5 years in the house, there are only minor scratches in the parquet so far. But that is exactly what characterizes a wooden floor. It can look a bit lively. Our parquet is oiled. If necessary, you can sand a scratch and "seal" the spot again with oil.

I say quite clearly: no We have had solid wood planks in the children's room for 3 years, there are small dents in them, but every floor gets those over time.

We also have solid wood in the living room, it has scratches too (mostly from the dog), but you don't see them that much because of the oiled surface. However, it would be too precious for me in the children's room, our son sometimes drops his dumbbells rather roughly, and that would leave huge dents. He also likes to leave wet towels on the floor, which is not so good for solid wood either.

Best regards Sabine

those are things I better not comment on now because they don't really relate to the floor question but the problem lies more with the occupant of the room