Buying a plot of land where a house previously burned down. What should be considered?

That doesn't seem to be a basement in the classical sense (completely underground), but rather a floor built halfway into the slope, right? Is it supposed to become living space then? Can you build new structures on that? Does it comply with the energy saving ordinance?

Yep, that was a granny flat with its own entrance before the fire. I think we would plan it similarly again. Good question about the energy saving ordinance... I guess we would have to insulate it again.... But that shouldn’t be a problem, right?

If, for example, underfloor heating is to be installed, the room height might be too low. Possibly the insulation of the basement against the ground is not sufficient enough. I don’t know if there are exceptions for half renovation, half new construction, or how this is regulated.

Good point, I hadn't given much thought to insulation under the basement yet. The report says the following about the basement floor, among other things:
"
Foundation: 8cm thick gravel blinding layer under the concrete slab including drainage etc., galvanized foundation earth with connection to the boiler room, PVC foil installed under the gravel blinding layer beneath the concrete slab.

Foundations: unreinforced strip foundations, B15, 30x50cm, concrete floor slab B15

... vertical insulation in the earth area according to DIN, horizontal insulation against moisture
"
That sounds uninsulated to me except for a moisture barrier. Would that mean I have to expect to insulate the basement floor from the inside? Underfloor heating would probably not be an option due to the additional height.
Since we are currently considering wall heating for the house above, that would certainly also be an alternative for the basement.

There are other options. For example, there are PUR panels for insulation. They insulate better at the same thickness than other materials. If the basement walls are properly insulated, a wall heating system is also possible. Don't bury your head in the sand. There are almost always possibilities.

tear down, dispose

yup! very helpful and well-thought-out comment. Definitely helps the OP.