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0 is a real number.
No. The square root of negative one is an example of an imaginary (not real) number. Pi is irrational, but real.
The question is confusing. The additive inverse of a real number is the same number with the sign changed. For example, the additive inverse of -5 is +5 (or simply 5); the additive inverse of 7 (which is the same as +7) is -7.
2 is a real world prime number.
It need not be. For example, a complex number as a percent of most other complex numbers, or any real number, will not be a real number.