Is space curved at the center of gravity?

[A.T.]

So the effect on the curvature from the surface of an object to its center decreases, as noted by inflection point located at the boundary between the grey and black shade ( I assume this boundary represents the actual surface of the object);

Curvature is related the 2nd derivatives. It is positive inside and negative outside (for a uniform density sphere).

however, the effects due to gravity remain at the center.

Gravity has nothing to do with these diagrams. You need to include the time dimension for that. See my earlier posts, and chapter 2 of this thesis:
http://www.relativitet.se/Webtheses/tes.pdf