A real number is irrational if it is not rational - meaning it cannot be expressed as a ratio of two integers. Numbers like pi, e, the square root of 5, and uncountably infinite more cannot be expressed as a fraction (ratio) of two integers, and are thus irrational.
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No. The sum of an irrational number and any other [real] number is irrational.
A negative irrational number can be thought of as an irrational number multiplied by -1, or an irrational number with a minus sign in front of it.
If an irrational number is added to, (or multiplied by) a rational number, the result will always be an irrational number.
Any irrational number will, eg √2, π, e.
Yes