As promised, here's the update. One day later, the damned problem has been fixed. Now the bike starts without any hiccups even at near zero temperatures (last night it was 7 C), without using choke.
For anyone in FSD, the guy's name is Khalid. He's Suzuki's authorized mechanic and his shop is just opposite to the Suzuki showroom on Narwala Rd.
I guess, he has a magic touch, even though he didn't have any feeler gauges for the valve clearance
One other thing he did was to drain to the fuel from carburetor using overflow drain screw