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No, it is imaginary. Irrational numbers are a subset of real numbers Real numbers and imaginary numbers are sets without any overlap.
Yes, imaginary numbers are a subset of complex numbers.
Real numbers are the subset of complex numbers with the property that their imaginary part is zero. Since the above number has no imaginary part, it is a real number.
A complex number has a real part and a (purely) imaginary part, So imaginary numbers are a subset of complex numbers. But the converse is not true. A real number is also a member of the complex domain but it is not an imaginary number.
Not necessarily. The square root of 4 are +/- 2 which are Real numbers, NOT imaginary. Although, since the Reals are a subset of Complex numbers, the above roots would belong to the Complex numbers.