No, it is not.
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If you multiply or divide an irrational number - such as pi - by ANY rational number (except zero), you will ALWAYS get an irrational number.
No, it is not.
No. sqrt(2)/pi is not rational.
A rational number is a fraction with an integer in the numerator, and a non-zero integer in the denominator. If you consider pi/2, pi/3, pi/4 (common 'fractions' of pi used in trigonometry) to be 'fractions', then these are not rational numbers.
A real number dosen't have to be a rational number as a real number can be rational or irrational i.e the root of 2 is irrational and real. So is (pi).