Most of the Moonlight Heroes are alternate selves of their respective counterparts, thus having a different Zodiac sign. But there are also exceptions in which the ML Hero has the same Zodiac sign as the original version, and it can be justified in the story because they are the same character, but went through a drastic change. The most obvious example of this case is Vildred, who went to the dark side and became Arbiter Vildred, hence why the two versions have the same Zodiac sign of Leo.
Rose is a clear reference to the Greek Goddess Nike with all that Valkyrie appearance and her feathered headdress. However, the most obvious clue to this is Rose's ultimate ability, named "Goddess of Victory" which also makes a pair of wings grow from Rose's back. In the myths, Nike is known as the Goddess of Victory and is closely associated with wings.
Judging from Kizuna Ai's backstory in the Hero Journal alone, it was stated there that Earth had been destroyed but she was found by Yuna in a disc and was rebooted. Plot Hole asideExplanation How in the world did Yuna find a disc from a destroyed planet? Sadly, we'll never get the answer when there's no side story that came with the crossover event, and if this backstory is taken as canon, then it could mean that Yuna and Tamarinne could no longer go back to their original world no matter how hard they try.