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.
Yes, the My Little Pony Friendship is magic episode Twilight's kingdom is involved in the rainbow power.
The My Little Pony Friendship Is Magic episode with baby twilight sparkle is calledThe Cutie Mark Chronicles"this is where the cutie mark crusaders ask twilight applejack fluttershy rarity pinkiepie and finaly rainbow dash (not in that order exept for rainbow dash she comes last)
The episode in which Ash gets the Rainbow Badge is called "Pokémon Scent-sation."
Pinkamena sits on Rainbow Dash in season 1 episode 25 "Party of One"
No. It is the last episode of season 3, but there will be a season 4.
Yes, the My Little Pony Friendship is magic episode Twilight's kingdom is involved in the rainbow power.
Yes. This has recently been announced.
When the cows come home
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.
According to the synopsis, it is about Rainbow Dash having to choose between the Ponyville relay team and the more competetive Cloudsdale team.
The Internet Movie Database (IMDB) is always a good source for info on videos, movies, etc. Equestria Daily is a good source for My Little Pony related news.
It might be, as it does center on Fluttershy, but we have no way of knowing for sure until the episode comes out.
The My Little Pony Friendship Is Magic episode with baby twilight sparkle is calledThe Cutie Mark Chronicles"this is where the cutie mark crusaders ask twilight applejack fluttershy rarity pinkiepie and finaly rainbow dash (not in that order exept for rainbow dash she comes last)
Season 1, Episode 1: Friendship is Magic
It is not known what these flashes of rainbow in the pony's eyes is supposed to represent, but this will likely be revealed in the Season Finale of Season 4 of My Little Pony: Friendship is Magic.
The episode in which Ash gets the Rainbow Badge is called "Pokémon Scent-sation."
Pinkamena sits on Rainbow Dash in season 1 episode 25 "Party of One"