What kind of stones are these and do they play a significant role?

24 times 100 cm, hangs from the ceiling, found a few more there, but still don’t know what it is or what role the parts play

24 times 100 cm, hanging from the ceiling,

Here rather: leaning against the wall. The measurement probably refers to the width and length, thus about 6 cm in height.

still don't know what it is

Me neither – because you haven't yet addressed the uncertainties I mentioned about what can be seen in the pictures.

You probably recognize the material as porous brick yourself. I initially thought of ceiling elements: those would be clamped, reinforced, and covered with in-situ concrete. And that would rather not happen in half-timbered houses.

As on the new photo, these probably are not such elements – but also not really suitable as precast flat lintels, although the measurement would fit above a 76 cm door in a 24 cm wall. For non-load-bearing interior walls, these bricks wouldn't make sense to me either.

I fear here, unfortunately, that a do-it-yourself builder simply installed parts "matching" the measurements freely, ignoring their intended use. I don't want to speculate on how lucky that can be in the long run.

To me, this smells like "DIY enthusiast without an architect (and without a structural engineer) got material cheaply" :-(

I only know it the way you described, actually. But if you torture the search engine a bit, you find the term "Hourdis slab."
Apparently, they were simply placed between steel beams (without reinforcement like in a "regular" stone slab) and poured over with concrete.

Why do you even bother after the statement in #5?

Why do you even bother after the statement in #5?

I am as friendly as I am not nice - both in an almost pathological dose ,-)

But if you torture the search engine a bit, you find the term "Hourdis ceiling".

I just wasn’t familiar with the term ...

They were apparently simply laid between steel beams (without reinforcement like in an "ordinary" stone ceiling) and covered with concrete.

... and in this case even the technique itself: according to the internet, this was even done on wooden beams, which I actually did not know.

Presumably a) the previous owner read about it or b) it was done this way in this house before and he then recreated it - regarding the shown stones, I stick to the assessment after the photos that these 1. are not original from the half-timbered house "era" and 2. are of more recent date in the sense of the 60s or even younger. But my feeling might be wrong, as said, the photos are indicators of unknown calibration.

Could it be that it is about the ceiling of a masonry base floor? The half-timbered house only starts above?

As for the clay tile elements, I would suspect that they were installed as a kind of lost formwork. A proven concrete ceiling was poured on top. This should then fulfill all static functions. In any case, the clay tiles with the cracks no longer bear any load, they are completely broken through.

Regarding the flush cistern: simply turn off the tap in the cistern and check whether the water level in the cistern is maintained over time or not. If the leak is on the way there, of course you won't find out that way, but in any case, I would start looking from the top and not from the bottom.

Although water damage should cause stains and not broken clay tiles. But as said, you don't know what is above. Rotten beams etc. could be pressing down from above, no idea.

Whereas water damage should cause stains and not broken clay tiles.

Yes and no: I do consider an explosive effect that turns hairline cracks into visible cracks quite possible.