Upgrading an old building with underfloor heating - experiences

Hi,
after having my eyes opened in another post here, I am now trying to read up on the renovation of our old building...
The house, built in 1952, is in an almost original condition. Now on the plan, among other things: new windows and front door, cavity wall insulation, and of course the floors.

Currently, a gas heating system with a low-temperature boiler and radiators is installed. Since my parents live in a similar house where the floors are always very cold, I would like to approach this differently.
My idea: there has to be underfloor heating and the radiators removed! For me, the easiest self-installable solution is the option with dry screed elements, into which you can lay the underfloor heating yourself.
Now the questions:
1. Is additional insulation needed towards the basement? Structure of the basement ceiling: concrete vault between steel beams, with wooden joists and floorboards on top. No insulation.
2. Is it more sensible to insulate the basement ceiling from below or to pull out the wooden floorboards, add a filling as insulation, and screw the screed elements onto the beams? Or have insulation material blown in?
3. The front door is also to be replaced, which is not a big problem, but how can I adjust the stair steps to the upper floor to the new floor height? It is a simple wooden staircase.

I look forward to your answers!
Best regards
Heiko

Good morning!

If I read the other thread correctly, it is about a) renting and b) initially the most necessary energy renovation.

If the floorboards are OK, I would be reluctant to tear them out. They usually make up the charm of old buildings. I would only refurbish them. Underfloor heating would be overkill for me at this point. If necessary, the basement ceiling can be insulated from below. But I am not a specialist in that.

Yes, the wooden floor would look great, unfortunately it is extremely noisy and since an apartment is to be created both upstairs and downstairs, that unfortunately won't work.
Best regards

Maybe over the ceilings. That you insulate from below and install soundproofing. It is also a question of where the sound is transmitted. In the end, the floorboards are removed and laminate with impact sound insulation is installed without much effect.

That's why I'm considering whether the layer between the concrete ceiling and the floor should be filled with insulation; that should provide both insulation and soundproofing... Has no one had any experience with that??