really confused with the last panel of the left 4koma. not sure what checking the weather has to do with anything. explanation if there is one?

Maybe she’s checking the weather forecast to see whether hell’s going to freeze over. After all, so far we don’t know where they’re living.

Well, where I live it's common to say "its gonna rain" when soemone days or does something out of character.
could be a similar thing.

So what's Tamaryu's face on the last panel on the right parodying?