The x-axis and the y-axis should always be perpendicular so that you can express any point in a 2-dimensional plane using an x value and a y value. They are perpendicular so that using them and visualizing is easier, so that x values have no impact on y values and vice versa, and so that formulas like the distance formula can be used. In general, right angles are much easier to work with than oblique or acute angles.
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Nope. It is complementary angles that add to 90 degrees.
x0 and y0 aren't lines. Do you mean x=0 and y=0? If so, they are the y axis and the x axis, respectively, and the answer is 90 degrees as noted above.
always 90 degrees
A right angle
There's always an angle that is 90 degrees