Who are the people of Madinah about whom many Hadiths have been narrated, and does this description apply to everyone who has lived in Madinah since birth and resided there, even if they are not originally from the city, or is it exclusive to the Ansar and the ancient inhabitants?

Yes, there are prophetic traditions (hadiths) that invoke blessings upon the people of Madinah and warn against intending harm to them. Among these are: "Whoever intends ill upon the people of Madinah, Allah will dissolve him as salt dissolves in water," and his (peace be upon him) supplication: "O Allah, bless the people of Madinah in their measures (of food)." The people of a place are its residents and those who live there, and the hadith addresses the general inhabitants of Madinah, not specifically the Ansar Companions and their descendants. Thus, anyone who resides in Madinah is considered among its people.