Yes, a very small proportion are.
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All integers are rational numbers. There are integers with an i behind them that are imaginary numbers. They are not real numbers but they are rational. The square root of 2 is irrational. It is real but irrational.
No, rational number are ones that can be written as a/b where a and b are integers. Irrational numbers are those real number that are NOT rational.
All integers and fractions are rational numbers whereas an irrational number can't be expressed as an integer or a fraction.
Every integer is a rational number, and some integers are perfect squares. These are the only rational numbers to have an integral square root.
Starting at the top, we have the real numbers. The rational numbers is a subset of the reals. So are the irrational numbers. Now some rationals are integers so that is a subset of the rationals. Then a subset of the integers is the whole numbers. The natural numbers is a subset of those.