trapezoid
not always
It has one pair of opposite angles that are equal but not two.
A parallelogram, or variants of polygons with 6 or more sides.
You need at least one pair of parallel sides. Most trapezoids have that.
all sides being equal
A square
2
1
A rhombus or a parallelogram would fit the given description providing the acute angles are equal and the obtuse angles are equal and that they all add up to 360 degrees.
A trapezium, or any one of irregular polygons of 5 or more sides.
No. Parallelograms have only 4 sides with 2 sets of parallel sides: they include squares, rectangles, and rhombuses (rhombi, diamond shapes). Because opposite angles are equal, each pair of parallel sides is equal in length. (For squares and "equilateral rhombi" all four sides are equal in length.)
it has more than one pair
Not sure about angels and parrellel, but a trapezium has four angles and only one pair of parallel lines.
There are many such shapes: a prism a cylinder a parallelepiped an octahedron a dodecahedron. Most polyhedra can have a pair of opposite a parallel faces.
trapezoid
trapezoids