No
There is no known backstory for Queen Chrysalis as of yet, and it has not been confirmed if she was or wasn't Princess Papillon. Princess Papillion appears to have been a fan-made version of Chrysalis and so is not a cannon character. It is unlikely that Chrysalis has any connection with the Rainbow Kingdom.
No, Queen Chrysalis from "My Little Pony: Friendship is Magic" was not originally Princess Papillon. Queen Chrysalis is a unique character created as the leader of the Changelings, while Princess Papillon was a character from early concept art and never made it into the final series. The two characters are distinct and serve different roles in the show's lore.
because she is a queen and she came first in a eqestria.
there is no princess in Costa Luna because it Costa Luna is just a make up place.
Costa Luna
So far there has been no mention of how Luna and Celestia came to be.
So far there has been no mention of the parents or any the mention of the origin of Celestia and Luna.
Princess Luna became jealous of Princess Celestia and tried to take full control of Equestria and bring everlasting night. Celestia was forced to banish her to prevent this.
The princess is any female relative of the king or queen; for example princess Margaret was Queen Elizabeth's sister.
the Mexican island where princess rosie lives
The daughter of a king and queen is called Princess.
No, the show is about friendship. Not boyfriends.