Renew electrical wiring? How to find out?

Hello,
my wife and I are thinking about buying an apartment, we already have one in mind.

During the viewing, I noticed that the fuse box is already a few years old and a [FI Schutzschalter] is not present.

Conclusion for me as a NON-electrician: Warning! Old cables, old network, might need to be redone.

I then looked in every room to see how many cables come out of the ceiling, there are always three cables, so there is no neutral earthing but each room is grounded independently, right?

With three-core cables, actually only the fuse box should need to be replaced, the cables should be fine, right?

I would like to save myself from having to replace the cables.

I would be very happy to receive feedback / clarification.

Regards,
Chris

As a complete layperson, you will not be able to assess this, and from a distance, you cannot say anything at all. The question is what kind of cables with which cross-section are installed in which circuits. Ultimately, you need to check a) whether the electrical system is still okay (insulations, etc. intact) and b) whether the circuits and their load capacity meet your requirements. This requires consultation and inspection by a professional. Even if an FI switch has been installed, it could be that it was retrofitted using very old technology. A "classic neutral conductor" would be a "negative proof" but a protective conductor does not necessarily mean that everything is okay.