Black Rabbit and Izayoi's relationship could not be good at first, in the Light Novels, groping her breast and legs when she was in shock after the battle with the Water God. She even went so far as to call him her nemesis. However, as time went by Black Rabbit's opinion changed and she has shown appreciation for him and his power and intellect.
Her opinion changed to favorable during the event of episode 5. When Izayoi declared that he wanted their flag to be in the stars Black Rabbit replied, "Seems romantic" and they both smiled at each other. The feelings were mutual as Izayoi's teasing of her could be seen as him holding certain affection levels for her, but could also be because he thinks of her as a toy. However, when she was injured in Volume 6, Izayoi became enraged, abandoned all his principles just to get back at His Highness.
However the two are considerd to be close. Izayoi enjoys teasing Black Rabbit and even remarks on taking her virginity. As for Black Rabbit, she shows great care for Izayoi and was greatly traumatized that he was injured severely just to protect her. Izayoi protected Black Rabbit from an attack from Azi Dahaka, and apologized to her for he could not be able to keep the promise of recovering the lost name and the flag. Black Rabbit was really happy and relieved to learn that Izayoi was alive during the trial period. That made her hug him so much while he was in bed that also made Izayoi very happy to the high extent to see Black Rabbit again.
She has also blushed several times when complimented or confessed by Izayoi. It is also heavily applied that Izayoi also cares deeply for Black Rabbit, as he always rescues her. He also told Black rabbit that her beauty is his type and that she is very attractive. In volume 5, he also said that even when he looks at every other girl, Black Rabbit will always be the cutest girl in his eyes, which caused her to blush.
Their feelings are mutual, for Izayoi caring deeply for Black Rabbit and for Black Rabbit seeming to have develop feelings for him, but doesn't realized this because she still doesn't have much knowledge for love, and that of Izayoi always teasing Black Rabbit for it being hinted that it is his way of showing likeness and affection for her. For it being of an affectionate mutual understanding. For now their relationship is a rather close friendship and being comrades of the same community with implications of becoming something more.
They both seem to have a close friend relationship. Shiroyasha thinks that they're "more" than friends, so she does perverted actions towards Black Rabbit as shown when Shiroyasha jumped right into Black Rabbit's chest. However, Shiroyasha is not afraid to criticize Black Rabbit but will defend her if the teasing goes too far.
After the destruction of the Moon Rabbit Community, Black Rabbit was adopted by Canaria. Canaria was seen as a mother for Black Rabbit and she admires Canaria greatly to the point her main reason for wanting to revive the community was to protect the home Canaria fought for.
Black Rabbit holds Leticia in high regard as she said that she was taught many wonderful things by her (Leticia).
Jin is like a little brother to her who she can not stop worrying about even if he is the leader of the current No Name.