Solid wood parquet on underfloor heating

What could still play a role for the installation method for me is that we removed the tiles but left the tile adhesive in. Using the hammer drill was too much effort for me. I wouldn’t have managed that for almost 100 sqm. However, the floor layer said that he would simply break off the peaks with the milling cutter and level the floor. I'm curious how well that will work.

So if you don’t want to work with battens and screwed planks, I would have a big question mark there.

For other installation methods, you need a smooth, spackled/leveled floor.

I'm not sure how comparable the situations are and am telling you for information how things are going with us:

The concrete floor here is quite "rough." As a layperson, I would have thought it needs to be smoothed first, but several craftsmen have convinced me that the Styrofoam boards (on which the heating pipes are clipped with small plastic clips) can be laid directly on the unsmoothed concrete (that's how it has been done now... "You can also throw your money away - but it's not necessary"). On the so far prepared underfloor heating comes (hopefully soon - due to Corona-related sick leaves, it is taking longer than planned) the (about 6cm thick?) screed, whose surface (as announced) will be smooth-spackled so that the 8mm thin wooden floor can be glued on.

At the moment, other craftsmen are walking on the exposed pipes again and I hope nothing gets damaged, but these jobs have to be done sometime. The whole thing is now taking significantly over a year instead of a few months o_O

Sure, filling under the screed is wasted money!

The area directly under the floor covering is always smoothly filled, or in the case of drywall systems, the raw subfloor

Sure, filling under the screed is money down the drain!

In the above-mentioned case, the question is whether the adhesive should be removed, or if it is enough to sand down the protrusions. I assume sanding down the protrusions is enough.

Floating version recommended, but I was just a bit influenced by the statement of several other parquet layers who had strongly advised me to glue it down.

I have now received an updated offer again. However, it has already become significantly more expensive, well more area and more expensive covering. However, he now wants to glue the parquet. I find that so-so. Apparently to decouple the floor covering from the substrate due to the cracks. Does that have to be?

I have now received an updated offer again. But it has become significantly more expensive, well, more surface area and more expensive covering. However, he now wants to glue the parquet. I find that so-so. Apparently to decouple the floor covering from the substrate because of the cracks. Does that have to be?

A bit unclear to me what you are writing:
"Glueing to decouple"? That doesn’t fit together.
"Cracks in the substrate in which underfloor heating is installed"? That doesn’t fit either...
If there are cracks, meaning the substrate moves, you can’t glue anything on that bridges over the cracks.