It means that:
a) The number is irragional, and
b) the number is not zero.
Since zero is rational, it isn't irrational, so saying that it is nonzero is really superfluous.
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It is an irrational number.
The product will be irrational.
Yes, always.
82 is not an irrational number because it can be expressed as the quotient of two integers: 82÷ 1.
Suppose a is rational (and non-zero) and x is irrational. Suppose ax is rational;write ax = b where b is rational.Then x = b/a, and x would be rational, contradiction.