Euclid's parallel axiom is false in non-Euclidean geometry because non-Euclidean geometry occurs within a different theory of space. There may be one absolute occurrence in non-Euclidean space where Euclid's parallel axiom is valid. Possibly as some form of infinity.
yes Not always! Parallelogram: A quadrilateral with both pairs of opposite sides parallel is called as a parallelogram. Rectangle: A quadrilateral with both pairs of opposite sides parallel and all the internal angles are 90o is called as a rectangle. Rectangles satisfy the condition of a parallelogram. So, all rectangles are always parallelogram. But, all parallelograms are not rectangles. Source: www.icoachmath.com
To construct a trapezoid you will need a quadrilateral with one pair of parallel sides.
The number of sides in a polygon can be three or any larger integer.
As far as I am aware, there is no such word.