Is a rhombus a parallelogram

Yes. A rhombus is a special kind of parallelogram. It's a four-sided figure that has all of the characteristics it needs to be called a parallelogram, plus the extra feature that it needs to be called a rhombus.

A parallelogram doesn't need to have all four sides the same length. If they are, then it can also be called a rhombus.

In the same way ... the rhombus doesn't need to have all four angles the same size. If they are, then the rhombus can also be called a square.