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Probably not. It has been said by the production team of Equestria Girls that Equestria Girls was meant to be a standalone, and not be connected to the TV show My Little Pony: Friendship is Magic.
It has not been revealed when Discord came to Equestria.
When the cows come home
yes
My Little Pony Friendship Is Magic - 2010 was released on: USA: 10 October 2010
Yes. This has recently been announced.
No. Wondercolt Archers is a fan animation.
No. Although he appeared in Equestria Girls, one of the writers has state that he will not be appearing in the show itself.
No. It has been stated that season 6 will focus on exploring Equestria.
The Equestria Games arc of My Little Pony seems somewhat similar to the Grand Galloping Gala arc of season 1. So it is logical to conclude that it will be right before or part of the season finale.
Yes.My Little Pony: Equestria Girls premiered in theaters in June 2013,In this movie Twilight goes into an alternate world where everyone is human but they are the same characters as in her 'normal' world. Once again though she uses the magic of friendship to save the dntire world including her own world.Also Equestria Girls: Rainbow Rocks is the upcoming movie this fall.
My Little Pony: Friendship is Magic premiered on October 10, 2010.