I would say Kuroe has just been dressing "Saika", she does bathe her after all, but... the chapter where Erulka attends to her does seem to imply that "she" hasn't been. Due to the constant transformations that would require Mushiki to also wear one because while magic may change the clothes it...
Nah. Just gotta stay in character to keep the secret even in private in case anyone eavesdrops. Saika herself is not kuudere.
The dichotomy is not explicitly mentioned here but it is pointed out in the books (in the exact scene this corresponds to).
We do get varying small glimpses into what she...