Who is God meant to be? I apologise for the theological sounding question, but I couldn't phrase it any better.

In Oyasumi PunPun, PunPun can see God whenever he chants 'Dear God, dear God, tinkle-tinkle hoy'

This character always has the same expression and is realistic to a point that it seems it has been copied from a photograph or similar media.

Is God based on the appearance of the mangaka or anyone in particular?
According to Japanese Yahoo! Answers, he is Kumatsuto, Asano's—the mangaka—close friend.

A customer review on Japanese Amazon also mentions Kumatsuto as the god (くまつとさん神様)

He is also mentioned in the manga's credits