Parallelogram
A shape with 4 straight lines in which there are 2 parallel and 2 unparallel lines is called a Trapezium.
A square
Strictly speaking, the answer is no. There is an implicit assumption that parallel lines refer to straight lines and, since there are no straight lines in a rainbow, there cannot be any parallel lines. The lines are concentric and so they never meet.
A trapezoid.
a regular square!
It is a plane shape bounded by four straight lines, a pair of which are parallel.
A right trapezium. A right trapezium. A right trapezium. A right trapezium.
A trapezoid has two parallel lines.
A rhombus has parallel lines but no perpendicular lines.
There is no shape that has sides that are all parallel to each other. That would just be a collection of straight lines.
Any shape that contains a section of a plane can have an infinite number of parallel lines in it.