Yes. go to the pastoria gym and one trainer should have it.
Chat with our AI personalities
Ace Trainer Shannon on route 221 has a Lopunny, inside the grass to the east
Eevee (Day or Night), Chansey, Golbat, Togepi, Pichu, Cleffa, Igglybuff, Azurill, Budew, Buneary, Chingling, Munchlax, Riolu, Woobat and Swadloon.
Yes, because whoever owns the egg when it hatches is considered the original trainer.
Azurill
You can get azurill in pokemon diamond and pearl by either breeding azumarill (or marill) or capturing it in the safari zone. :]