"Omika" is something like "Great Mika", no? The "O" being from "Ou", "King/Royalty", right?
So, Nao was being jokingly polite formal with Mika and her "fragility".
And Nao is so nice, no wonder Mitsumi is that jewel with family like that.
Now, "that" girl ruins this manga.
It's a shame that she existis in this story, frankly, I never expected to see this type of character in this super comfy series. Shima made mistakes WHEN HE WAS A KID! He learned, she changed. But her acts like that... I hate this character.