Yes,
However, it is not defined that way. It is defined as a number that cannot be expressed precisely as a ratio of two real numbers (a fraction). But that is equivalent to a non-repeating decimal.
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an irrational number
Yes.
An irrational number can be represented by a non-terminating, non-repeating decimal.
An irrational number by definition can not be exactly represented by a decimal that terminates or recurs. The moment a decimal terminates, or settles into a repeating pattern, it is rational.
Every irrational number can be represented by a non-terminating non-repeating decimal. Rounding this decimal representation to a suitable degree will provide a suitable approximation.