Not much is known about Tsukuyo, but that doesn't change the respect the rest of the Five Supreme Swords or Nomura has for her. It does not appear that Inaba Tsukuyo is very good at making friends because she, as well as the rest of the Five Swords and Amou, lacks the knowledge of friendship.
Not much is known about their standing at the moment. However, it appears that she knew of him to a certain extent. Despite her seemingly being a dangerous person, she does not show any real murder intent in front of Nomura.
She declared that Nomura was her fellow student and she tends to be irritated and show more emotions when he is nearby, demonstrated when Nomura did not pay attention to her story and went to the roof instead. When he saved her from Amou Kirukiru, she questioned this as they weren't friends before believing he wanted to befriend her, which caused her to get flustered and blushed as he was confused by her words. She said she would accept if he was insisted but Nomura replied he wasn't trying to be her friend, to her surprise. However, he did tell her what it means to be someone's friend, which made Inaba think of him in a new light.
After Nomura managed to defeat Amou Kirukiru, Tsukuyo decided to become his next martial art teacher, and was later accepted by showing the upgraded Madan. Nomura sees her as a worthy teacher and rival who surpasses him, though he might easily surpass her due to his skills and her weak body, as shown when he defeated Amou where she struggled greatly.