About Rinka’s comment on “Keigo” (p. 3): Sumire actually asks the question (p. 2) using なんすか (nan suka), a shortened form of the polite 何ですか (nan desu ka). Shibuya then uses this to tease Sumire as she points out her “lazy politeness.”
Aside from this detail, the exchange here revolves around the senpai-kouhai paradox: Sumire is the manager, is older, and has experience as an idol, but she has/tries to show respect to Rinka, who is effectively her senpai when it comes to the whole “Onee-san” thing.