Final update
The electricians confirmed our hypothesis that the PE line was not grounded. They opened up all the junction boxes, from our house to the main fuse board downstairs, and found that extremely low quality, thin and single core wire had been used for earthing. This same quality wire was used for earthing for both the low current outlets, as well as the high current ##(11~\mathrm{A})## outlet. A few pictures of the wire when they took it out:
Note that it was already snapped when they removed it. Also notice the condition of the insulation.
So, we went to our local trusted electric supply store and bought good quality ##1.5~\mathrm{mm}^2## wire, as recommended by the electricians. A comparison of the old and new wires can be seen below:
The previous wire was completely replaced, from our house to the main fuse board, with the new wire. Thereafter, I checked the PD between neutral and PE with my multimeter; it was around ##0.3~\mathrm{V}## in all outlets.
The electricians also showed that the earthing wires inside our house are made of that same low-quality wire. We will be changing them in the coming days.
Once again, PF has helped me a lot in diagnosing the problem. Also learnt a lot in the process. Thanks to everyone who participated in helping me out, especially
@Baluncore,
@Averagesupernova,
@Lnewqban,
@Rive,
@hutchphd, and
@OmCheeto for your precious time and input. Also, a massive salute to the moderation team, without whom the site would not have been functioning as it is today.