Do cockatiels lose their nails?

I'm from Brazil. A lost cockatiel showed up in my parents' house. The cockatiel has only one nail. Two peope are claiming the animal saying they're the owner.

Is it possible that the cockatiel has lost nails during this time he went missing?

Another question: how far can these animals go? People who are claiming the cockatiel are from distant neighbourhoods. Is it possible that the bird flew several kilometers (5 - 8 km)?