Hey! Here are the answers to your questions:
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"Do you have to beat the Elite 4 to recieve the Eon Ticket through Mystery Gift?"
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No, you need at least the 5th badge.
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"Is the e-Reader proved to be compatible with the Game Boy Player?"
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Yes, duh. I've already answered this question before for you.
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"Is the e-Reader region locked?" (meaning its only able to send data to games from the same region as it)
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Yes, an English e-card may not be sent to a Japanese Game. You must get a japanese e-reader for that
Now, there you go, again. =/