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Not necessarily. A parallelogram is a quadrilateral with 2 sets of 2 parallel sides. Only rectangles and squares have right angles as all four angles - a rectangle is a "special" parallelogram that has all four angles equal; a square is a "special" rectangle that has all four sides of equal length.
a quadrilateral
It can, but they can also all be the same.
A rectangle is generally defined as a quadrilateral with four right angles. No rectangle can have four different side lengths by that definition. Finding the area of such a shape is therefore impossible.
A square, by definition, must have four right angles. A plane shape with 4 right angles which is not a square is a rectangle.