An ad-hoc idea for testing 2D mesh inclusion:
If you took the closest three points to each test point, you could see if that combination of three points was an existing combination in the sets of vertices for each mesh face. If so, it sits on a face. If not, it falls off the mesh (in a hole or outside).
I see your point say. but I didn´t understand the part "that combination of three points was an existing combination in the sets of vertices for each mesh face". I don´t figure out how to get that.
I found a method on the Rhino SDK, RhinoIsPointOnFace, that may work.
have you tried it?