You! Do you like pretty Asian girls? Do you like metal mixed with a certain amount of bouncy pop? Do you like Nazis? All answers to those questions can and will be used against you in court, but in the meantime...
I'd recognize baby metal anywhere. Didn't even have to click play lol. What about Nagash's theme song: Reign of Darkness by Thy Art is Murder. One of my favorites for deathcore Sunday, which was 3 days ago but I listen to it all the time.
Afraid not, they only just came out with this song. They're older in the sense that the members look to be in their twenties, rather than being around sixteen.
But there's a LOT of heavier idol groups kicking about. Probably the earliest was BiS, although their image and music was very different from Babymetal's, and since they appeared around the same time I'm guessing it's coincidence, rather than one inspiring the other.