Hydraulic balancing, disable single room control?

Our entire house was too hot and too cold this spring (that's when we moved in)...

That is normal in the beginning. Especially since you haven't had a heating season yet. Construction moisture adds to it. Reaction of underfloor heating, insulation, and so on...

What actually happens if I simply unscrew the actuators? Then I am basically looking at a small pin that protrudes from the HKV.

Is the flow completely open on the side of the [Stellantriebe]?

That's how it should be done.

Is the flow completely open on the part of the „Stellantriebe“ then?

Whether you remove them completely or leave them on with the visible red ring is the same. Open is open.

Only I had then fully opened all the Taccosetters (with visible red ring of the actuators!) and still the flow did not noticeably increase...

That is why I wanted to dismantle the actuators to be completely sure that the valves are then fully open.

The flow rate is limited by your circulation pump and the flow resistance of the underfloor heating pipes (caused by the length).

You only have a certain (finite) force F that can act on the system and this is distributed across all heating circuits.

But yes, feel free to remove the motors completely.