I see no reason to replace the door. My thoughts...

1. Remove the existing door knob and latch mechanism.
2. Work wood (Elmers) or polyurethane (Gorilla) glue into the cracks where the veneer has split on the inside door face. There are a lot of ways to do this. Google "work glue into cracks". Then, clamp tightly until the glue dries. Sand the door face smooth after removing clamps.
3. If screw holes holding the latch mechanism to the door edge are stripped so that the screws no longer hold it tightly, google "repair stripped screw hole in wood". There are a lot of ways to fix those. For example, one option would be to glue tightly-fitted wood dowels into the holes and drill new screw holes.
4. Secure the strike plate to the door frame as well. This also can be done with dowels, or simply using longer screws.
5. Repaint door.
6. Install new door knob kit, which should include new latch mechanism.