Any polygon with 4 sides is a quadrilateral
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To determine if it is possible to draw a quadrilateral given four side lengths, you can use the triangle inequality theorem. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. If this condition is met for all combinations of three sides using the given side lengths, then it is possible to construct a quadrilateral. If the sum of the lengths of any two sides is equal to or less than the length of the third side for any combination, then it is not possible to draw a quadrilateral with those side lengths.
Because a square is a regular 4 sided quadrilateral
What do you mean by "length" as different from "side"? The multiplication will result in a number, that's it! Without knowing the angles and or the lengths of the other sides you have insufficient information to make any conclusions as to what that number represents. But if it is a right angled quadrilateral (a rectangle) you get the area.
It is a trapezoid which has 1 pair of opposite parallel sides of different lengths
Not necessarily; it is a parallelogram - a rectangle is a parallelogram in which all angles are 90o. It could also be a rhombus - a rhombus is a parallelogram with all lengths the same; a square is a rhombus in which all angles are 90o.