it not a straigh line
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== == yes. suppose the quad ABCD has AB and CD equal and parallel. Then the triangles ABC and CDA are congruent by SAS axiom; so the quad is a parallelogram
quad with at least a pair of parallel lines
A square and a rhombus
A quadrilateral is any figure with 4 sides. ("quad" = 4, "latus" = side). It doesn't have to have any parallel lines. If it happens to have two sides that are parallel, then it's a trapezoid. If it happens to have two pairs of parallel sides, then it's a parallelogram. Common parallelograms are rectangles, squares, and kites.
No, because quad means four (4) and lateral means sides. Any four-sided shape is a Quadrilateral. But the sides have to straight and a two-dimensional (2d). Some quadrilaterals have two (2) parallel sides, like a parallelogram.