Mann, this really bring back about Hayate. Make me want to reread Hayate again, hahahaha.
All of pieces mystery still unclear, we can only know thats Tsukasa has strong bond with moon. Her surname is Tsukuyomi the name of moon god in Shinto. She has moon stone in her room, as Chitotes states it to ease her. She has knowledge in Japan history really well like she has been there before (we can now this from chapter Tsukasa and Nasa went to Nara).
When Nasa ask why she marry him to Tokiko told him to aks to Tsukasa himself, and tsukasa didnt answer his question. And we still dont know what kind relationship Tsakasa has with Kaguya. This is Comedy manga but feel like mystery itself. Bring my memory back about Hayate no Gotoku.
So maybe next chapter come with POV Tsukasa and about her past, Hope soo.