Your skink is very young, maybe a month old. It is also a Halmahera form of the species called Indonesian, so a Tiliqua gigas gigas. Calling it a New Guinea blue tongue skink is a sign of not being aware of what kind of skink they have, and I highly doubt they bred it themselves, but that's beside the point.
Feed it daily for now, but if he refuses to eat some days, no need to worry, and if he refuses often then just cut offering food back to every other day.
Shedding is pretty individual at this age, but I would expect it once to twice a month.
The absence of hemipenes at defecating is not a sign of it being a female, especially not when this young, not all males pop them when defecating, and at this young an age there are no real clues to look for in determining sex.
Keep his humidity up (around 60-80%), or give him access to a humid hide at all times.
Good luck, and have fun with your little guy!
Breeder and keeper of Meraukes from 2010 to 2022.