It is very common to use, but it is not the only variable you can use.
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Not always. It could be a constant. For example x is one variable, and y = x-2 is another variable. Then x - y = x - (x-2) = 2.
Yes. A variable by itself, or anything that contains a variable, would be a variable expression (unless the variable cancels out, as in "x - x", which always has the same value).
The independent variable is always on the x-axis of a coordinate plane. The dependent variable is always on the y-axis. This is true because y always depends on x.
By convention, 'x' is almost always the independent variable, but it doesn't have to be.
x=3 means that the x variable always stays constant, so the y variable can change as much as it wants, but x will always be 3. on a graph, this would like a vertical line. (It should be perpendicular to the x variable's line...if that helps a visual:P)