Is there an actual legend of a moon princess?

Answer 1

Yes. In Japanese mythology, there was a story of a Princess Kaguya. It is sometimes called "The Tale of the Bamboo Cutter" or simply "Princess Kaguya," and is one of the oldest known Japanese stories.

Unlike the Sailor Moon S movie that featured a character of the same name, the mythical princess from the moon was found inside a glowing bamboo stalk by an old, childless bamboo cutter. The princess had glowing hair and became known for her beauty. Though the bamboo cutter and his wife tried to keep knowledge of her from the outside world, eventually several princes came to ask for Kaguya-hime's hand in marriage. Kaguya-hime said she would marry the one who completed a task she gave him; all either failed or deceived her in trying to complete their assigned task. The Emperor also came to ask for Kaguya-hime's hand in marriage, but she refused him repeatedly.

The Emperor persisted in his proposals, but was unaware of Kaguya-hime's strange behavior at home while looking at the summer moon. Eventually, she revealed that she was actually from the moon, and would one day have to return to her true home. The Emperor tried to stop those from the Moon from taking her away by having guards surround her foster parents' home, but she was still taken away--though not before giving her heavenly robe to her parents and an elixir of life to a guard to give to the Emperor along with a note.

The Emperor was very saddened when he heard about Kaguya-hime's leaving, but refused to take the immortality-giving elixir of life and instead sent an entourage of guards to the top of what is now known as Mount Fuji to burn it.