Pi is both an irrational number and a transcendental number.
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Pi is an Irrational number, which is one of the two subcategories of real numbers.
To any set that contains it! It belongs to {-15}, or {sqrt(2), -15, pi, -3/7}, or all whole numbers between -43 and 53, or multiples of 5, or composite numbers, or integers, or rational numbers, or real numbers, or complex numbers, etc.
To any set that contains it! It belongs to {-22}, or {-22, sqrt(2), pi, -3/7}, or all whole numbers between -43 and 53, or multiples of 11, or composite numbers, or integers, or rational numbers, or real numbers, etc.
Yes. For example: pi - pi = 0
Real, complex, quaternion, etc. But more specifically it's a transcendental real number, not being the root of an integer polynomial (and certainly not the ratio of two integers).