Every rectangle has those qualifications.
That includes squares.
4 sides and 4 angles
A non-square rhombus is.
It is a rectangle unless all sides are congruent, in which event it is a square.
Normally, none.
A shape with parallel sides but no right angles is called a parallelogram
That's a rectangle (possibly a square). If two sides are parallel, and all angles are right angles, then the other two sides must be parallel also.
Draw a parallelagram this has the opposite sides parallel and no right angles
trapezoid
A rectangle has 4 right angles and 2 pairs of parallel sides.
A rhombus has 4 sides of equal length, opposing parallel sides, and no right angles
It may have no right angles, and certainly no parallel sides.
The shape you are looking for is a quadrilateral. If you have a square, all angles MUST be right angles. A parallelogram can also have 4 equal sides in length and parallel sides, but a parallelogram doesn't have right angles.