A Channel/WMG

Satou is an Older Expy of Housaka from Minami-Ke.

 * Or the two are somehow related.
 * Similar in looks and creep factor.
 * And voice! (Ono Daisuke)

Run is an alien.
She doesn't tan or even get sunburned, for one thing. And her Ahoge is an obvious antenna. She isn't stupid, just unfamiliar with human customs. Her home planet has lower gravity than Earth, which is why she occasionally leans over railings too far and almost falls.

Kitou is Tooru's mom.
She looks a lot like her, and she (Kitou) told her that she (Tooru) always helps her, but maybe it also means that she helps her at home, too.
 * Unless that was another relative, Tooru's mum appeared in episode 5, so jossed?

Tooru is abused at home.

 * She is obviously underfed, can't buy herself a swimsuit (and has to wear Run's hand-me-downs), and considers swinging a baseball bat around a valid method of communication. And those long sleeves? they hide injuries on her arms.
 * The moments when the sleeves come off her arms seem to be fine though. And yes, skinny people do exist.
 * She is pretty insecure about her height and physique. Maybe she was teased or bullied a lot in middle school.

Yuuko is an alternate version of Mio

 * Wasn't there even a reference or a lampshade about this in one of the episodes?

Run was trying to tell Tooru something when she took her to that "Toy store".

 * Call me crazy, or more likely perverted, but i can't be the only person thinking that. And she did seem to find it awful quick...