The domain can be anything you like: a single element, all real numbers, all complex numbers, etc.
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It is -12.8, -6.4, 0, 6.4 and 12.8
It is difficult to say because of uncertainty as to what xx-4 represents. x2 - 4 = 4 gives x2 = 8 so x = ± 2*sqrt(2)
yes. it is a function
If it were written in a book of some sort, fx or f(x) is read aloud as "f or x". "f" is a function of some variable, "x". By function it means something happens to x e.g. x2 or 3x+4.
It depends on the domain but, if the domain is the real numbers, so is the range.