Is the grandmother Takeshi's mom, or Matsuko's mom?
Matsuko's mom, it isn't uncommon if the husband refers to his mother-in law as mother, as in The Flintstones, Fred refers to Mrs.Slaghoople, as Mother Dear.
Who found Nonoko at the mall? For a long time I assumed it was Toshio's mother, because we'd last seen Nonoko helping Toshio. But I'm not sure of that anymore. Toshio is never seen again after that one scene; we don't see him in the car with Nonoko driving away, and we don't see him at the house with "auntie" where Nonoko waits for her family. And when the family gets back to the mall and asks an employee about Nonoko, the employee mentions Nonoko meeting a woman, but doesn't mention a little boy. Also, Nonoko is said to recognize the woman. This could be interpreted as Nonoko being really friendly, but in the absence of Toshio I get the impression that Nonoko really did know this woman (who is not the same person as Toshio's mom.) Maybe she's a relative or neighbor? I'm not sure.
It is likely she is an aunt or someone really close to know the kids.