Jesus Christ, the amount of hate for the mother, for all we know that is HIS daughter and the mother broke off the relationship to not get in the way of HIS painting career or whatever.
She could be lying about the age.
As for looking for an apartment, we don't even know if she's looking or not and the "ideal apartment" comment was just a joke.
They were going out and by the 3rd friend interaction they all were obviously best friends, why would she not be happy/playful.
PS: I still thing she's her daughter, I saw a strand of hair that had the same curvy way, plus the hair goes the same way as Takaharu's, and the opposite way of her mother's