Just a bit about "mom" and "my mom." It's kind of hard to see right away, but if you were referring to your mom who does not otherwise have any relationship with the person you're talking to, you would say something like, "uchi no okaa-san" or something similar instead of just saying "okaa-san." It's a subtle difference in English too. There's a slightly different nuance in saying, "Mom said she wanted to see you" and "My mom said she wanted to see you." So this makes Nao-chan think that Ryuu-chan is familiar with Tama-chan's mom in more than as a mere acquaintance, which in turn makes the relationship between Ryuu-chan and Tama-chan much closer.