The answer will depend on what it is to be multiplied by. Since this part is missing from the question, it is not possible to give a sensible answer.
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Every rational number does.
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.
At least one of the factors has to be irrational.* An irrational number times ANY number (except zero) is irrational. * The product of two irrational numbers can be either rational or irrational.
A mixed number is a rational number. Mixed numbers are not a rational number but many of them.