There is no reason and probably impossible to get all the old veneer off cabinets of this build quality. If it is still glued done firmly it can be glued over. Wood to wood bond is always good. Just need to give it a good sand to get the oils off and you are set.
The fill is Wonderfill by Rockler Woodworking. It is a really good fill for this type work as it is wood dust in some liquid. So again wood to wood gluing is accomplished. I have used it a many projects with great results.
Gary