This is just unacceptable that a small engine like that of a cultus is blowing gaskits.
Just goes on to show the shoddy quality Suzuki is forcing us to accept.
For your problem, yes the head does need to be "faced" to ensure that it sits straight on the cylinder block and seals every thing shut.
The cylinder block itself needs to be leveled for the same purpose.
However I am not sure how did the mechanic conclude facing was required without using very precise instruments.
the whole point of having a gaskit is to account for the small variations in leveling between the two surfaces.
I suggest that you get 2nd and 3rd opinion, AND before you fix the gasket
FIX the cause of overheating which caused the first gasket to blow.