Yes and it is a vertical straight line parallel to the y axis
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No, but cos(-x) = cos(x), because the cosine function is an even function.
y < 1
X - Y^2 = 1 - Y^2 = - X + 1 Y^2 = X - 1 Y = (+/-) sqrt(X - 1) now, X is represented as a function of Y. Function values are generally Y values.
3
y = x2 + x = 0 x (X + 1) = 0 x = 0 is one solution x = -1 is the other