The cold start issue was with the ECU ignition IC. It was fried due to some short probably. Had to have the ECU repaired to resolve the problem and since then have not had any problems on cold start.
The RPM drop issue on fan/ac/headlight load was actually due to a faulty TPS sensor that was giving faulty reading to the ECU. Issue was resolved after replacing TPS.
Fixing the relay with chor switch wiring made no difference sadly as there was no such issue with current drop.