The bottom part is the dress guard. De-laminated wood can be glued back down. Clean the areas to be glued as best as you can with a little water then work the glue between the layers with something thin and clamp it down until it's dry. It usually takes at least 24 hours to be safe to unclamp. If the veneer is bubbled you may need to cut it to force the glue between the layers then clamp it.
Small areas of missing veneer can be replaced but the pieces missing from your top are large enough that repairs will be obvious. It will be almost impossible to just replace the missing pieces and have the color and grain match. I have a cabinet in slightly better shape that I will be starting on soon and I decided to replace the top veneer on that one.
The wood your cabinet is made from is quartersawn white oak. The wood under the veneer is a cheaper hardwood and won't match the rest of the cabinet.
If you decide to replace the veneer, save your old veneer for future repairs on other cabinets. It's easier to match old wood with old wood.
It takes time to restore an old cabinet but the results are worth the effort.
Rodney