Rewiring a flat (apartment) with concrete walls
I would focus on replacing the consumer unit.
Once you have RCDs (or better: RCBOs per circuit), the state of the wiring becomes less critical.
As far as earths, the fact that your wiring was done inside pipes (conduits) is very important.  Generally the pipes are installed before the wires are, so it's no trouble installing additional wires (or pulling all the old wires out and replacing with state-of-the-art wires).
Carrying earth on the metal pipe is perfectly fine.  Or, a yellow/green earth wire can be pulled into the pipe.  Either way is fine.
In fact, the old way of using metal conduits is superior to modern methods.  They stopped doing them because new ways are cheaper.
So my advice is to make the most out of the existing conduit in the wall. A variety of surface conduit methods can be used for new outlet locations not currently in the piping network.