The model is probably a sheet body and/or it has geometry errors.
Open the model file, start the examine geometry command, turn on all the body checks and the self-intersection face check, window select around the entire model (this will select all the faces and edges along with the solid/sheet body(ies)), and press the examine geometry button. If any of the tests fail, you will need to edit the model so that it passes the tests.
This is either a case for GTAC, or you upload the model here...
In the first image, NX notes "Solid body( in group) selected" and yet still the volume is zero.
Can you check if all the face normals point outwards from the solid ?
press Ctrl+ I, set the selecttion filter to Face, drag a rectangle around the body, OK
Dismiss the info window, all the arrows in the graphics should point out from the volume.
If you leave the tolerances alone, the measure body works after the thicken command, but not after the "move face" command. "Move face" should not invalidate a simple model like this; I'd suggest showing it to GTAC.
yes, this is a case for Gtac.
even if the model is built in a very complicated way, it should not become corrupted.
This model should rather be say 7 features.