Since this is going to be a very different take on the series as it will focus on Twilight Sparkle and her five friends from her school, how should the six of them get the keys to unlock their Rainbow power?

They won't

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Then how would they defeat Tirek?

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They would get the keys in their own unique adventure, proving element their elements true.
Like say Twilight trying to prove to herself that she became a good friend and tries to properly befriend Nectar, and gets a gift from her that is her key later on.
Or MoonDancer finding the courage to speak truth about something thats is hurting people. Or to simply correct someone who is simply wrong but makes her look like the "Umm actually" pony.

How I see it, they're destin to get the keys, just the how is different.