Do injuries on pokemon carry over to their evolutions? Like if a Bulbasaur had a scar/wound on its face (or anywhere), would the injury still be on the Ivysaur it evolves into? What would happen with something more serious, like a broken leg? And what about when pokemon lose body parts upon evolving, such as Kadabra’s tail, or Servine’s legs?

Yes, actually. While evolution seems to resolve minor injuries such as the scratches and bumps caused by battling, permanent or serious injuries—such as missing limbs, scars, and even status ailments—carry over to a pokémon’s new form. In cases in which a pokémon naturally lacks certain limbs in their evolved form (as in the cases of kadabra or servine, as you’ve noted), they may still carry scars roughly where the body part would have been. For example, if a kadabra loses its tail, it will carry a scar on its lower back and pelvis as an alakazam.

Why is a whole different subject. Evolution is a complete metamorphosis; a pokémon’s physical attributes are basically rewritten based on what’s dictated by their genetic code. By all accounts, you would think their evolved forms would become whole and fully healed, but for whatever reason, that’s not the case. Researchers have tried since practically the advent of pokémonology, but it’s still a mystery to this day.