No, it's a decimal number. 1,4142135623730950488016887242097
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Yes and it is 2
Yes, the whole idea of taking the "square root" of a number is, for example for the square root of 2, to find the number that, when squared, gives you 2. if you try to do both, they cancel each other out.
The square root of 2 is an irrational number because it can't be expressed as a fraction
If the square root is a whole number, then the square of the square root, the original number, is also a whole number; all whole numbers can be expressed as themselves over 1, and so are rational numbers. The answer is thus any square number, ie the square of the natural numbers: 1 (1²), 4 (2²), 9 (3²), 16 (4²), etc.
Some square roots of whole numbers are integers, some of them are irrational numbers. The square root of four for instance is a rational number, 2. The square root of two however is an irrational number, approximately 1.414211356.