Simply plot the irrational number at it's approximate location on the number line and label the irrational number.
For example, if you were to plot pi on the number line, you would plot it at about 3.14 and label it with "π" (the pi symbol, if it doesn't show up)
Another example is if you want to plot the square root of 2 on the number line. You would plot it at around 1.414 and label it with "√2"
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There is no such thing as an irrational number line.
The same as you would a rational number. Its distance from zero will represent the number, whether it is rational or irrational.
If you can express a real numbers as a fraction (with integers in the numerator and the denominator), then it is rational. Otherwise it is irrational.
Yes. In fact, a number line would be full of an uncountably many infinite number of discontinuities (holes) without them and hence would not be a line, so in fact irrational numbers MUST be placed on the number line in order for it to exist.
It is rational, as it is possible to express it as a fraction.