I haven't had the time to translate all of that, but when it happens a little icon will pop up on the bottom left corner of your screen. Just click that and get your number to be entered into the tournament.
Not everyone who gets a number will go into the battle royal though. I'm assuming who gets into that stage is determined based on their battle rank throughout the week. The higher your battle rank the more likely it is you'll get into the battle royal.
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