From an experimental point of view, you will probably find some discrepancies in the literature, especially when using atomic force microscopy as main characterization tool and comparing 2D materials deposited on various substrates (Si, SiO2, sapphire,...) and obtained with various techniques (as deposited by PVD/MOCVD, before/after transfer, exfoliated from bulk counterpart, etc.).
I guess it can be safely assumed that the thickness of a monolayer lies in the 0.5 - 1nm range.
Monolayer means one atom thick system. These systems exhibit strong spin orbit coupling. Therefore, we get a buckling along the z direction (perpendicular to the plane). Please look into the first principles based works.