Hello people, I've been so busy and couldn't update lately so here is an update.
I cleaned up wiring and removed all the burnt, sparking shorting wires just to make sure if that could help but my problems existed. To my surprise, I started using soft pedal keeping car under 4k to 4.5k RPM and this sweet Mini ended up giving 11 km per litre, I mean WOW. I went ahead and pulled out O2 sensor yesterday, cleaned it by dipping in petrol for 9 hours. Let's see if it improves any more mileage.
Now the main problem I had about starting in 3rd gear when cold. Since after wiring stuff, time reduced to 3-4 minutes before car starts shifting. Since last 2 days what I'm doing is I'm carrying a Lighter. before driving I heat up the gear card for about 10-15 seconds using lighter. Wait for another 20 seconds so it's circuit heats up from inside and WOW car starts fine and gears shift perfectly from the start.
I'm definitely going to install 1 or 2 small yellow bulbs over that transmission control card now with a timer of 20-30 seconds.