How to determine the place of a malfunction if the phase in the communal apartment is at zero?

I read a lot on the internet, but did not find an answer to my question. The question is: can a phase at zero mean a wiring fault and how to check it?
I want to hang a two-contact chandelier. Komunalka, its own meter, the wiring is old. The phase is common, and the zeros go to the switch. Three wires on the ceiling are not connected to anything, but the indicator screwdriver glows on all three wires, on the general (phase) brightly, on the others dimly. And in the switch, two zeros from the ceiling also glow. Although the room turned off everything and the phase should not have come to zero.

If we assume that the zero in our apartment is common and the phase from the neighbors could come to me, then it is not clear why only on the chandelier, because in sockets it is zero as it should be.
Perhaps this is capacitive induction. But how to make sure that the insulation on the wires is not broken?