No, they are not related. Perry isn't even her real last name. It's Hudson. Perry is her mother's maiden name.
No, she's not her mother. Katy Perry's mother is Mary Hudson.
No. She is the daughter of minister's Keith Hudson and Mary Hudson. Perry is her mother's maiden name.
No, she does not have a son or a daughter.
It was her mothers Maiden name (her name before she was married) :)