A four-sided polygon with opposite sides parallel could be a square, a rectangle, or a rhombus.
If it has one pair of opposite, parallel sides, then it is a trapezoid. If it has two pairs of opposite, parallel sides, then it is a parallelogram.
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A quadrilateral is a polygon with four sides. A parallelogram is a quadrilateral in which the opposite sides are parallel.
The parallel sides of a polygon are sides that are segments of parallel lines. A polygon need not have any parallel lines. A triangle, for example, is a polygon that cannot have parallel lines.
A rectangle is a quadrilateral with opposite sides parallel and congruent and four right angles. If all four sides are congruent, it is a square.
Yes, it has sides that are straight line segments. Exactly one pair of opposite sides is parallel. Polygons do not have curved sides.
Every 4-sided polygon in which the opposite sides are parallel is a parallelogram. Opposite sides are equal too, but it's not necessary to make that an explicit requirement, because if both pairs of opposite sides are parallel, then they also wind up being equal.