Is it permissible to inform the girl and her father about the true nature of a suitor who is well-known for his bad manners and reputation, given that he is skilled in flattery and the girl's father is wealthy?

If you are certain about the young man's poor religious commitment and character, then there is no blame upon you for informing the girl's family about the truth of his situation. This is considered offering sincere advice to Muslims, which is religiously required, based on the Prophet's (peace be upon him) saying: "Religion is sincere advice." What you have already done is sufficient; there is no need to send messages or do anything further.