Yes.
Any number which can be written down to all its places exactly is rational. A proviso is that the base (most commonly base 2 or base 10) must also be rational. Any number which is the ratio of two rational numbers (such as 1/3, or 186/100) is rational.
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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.