Oh, dude, let me break it down for you. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers. So, if you can write 5.12 as a fraction, then it's rational. Spoiler alert: you can totally write 5.12 as 512/100, which means it's a rational number. Like, no big deal.
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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.