If the idea is to continue repeating the same pattern, then it is not a rational number, because a rational number will repeat the same digits over and over again - for example, 0.505050505... or 0.550550550550550... If there is such a repetition, it is rational; otherwise not.
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Yes.
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It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.
Yes. Any rational number divided by another rational number is also rational.