Is a rhombus always a trapezoid?
Yes, a rhombus is a special type of trapezoid.
A trapezoid is a quadrilateral which has one pair of opposite sides parallel. As long as any quadrilateral has that property, irrespective of what other properties it may have, it is a trapezoid.
In a rhombus, the opposite sides are parallel. If two pairs of sides are parallel, then one pair of sides is obviously parallel, meaning the shape is a trapezoid.
The other properties concerning the lengths of the sides, the size of the angles, the properties of the diagonals, etc are what makes the trapezoid into a rhombus.
In the same way the following are all trapezoids:
Parallelogram, rectangle square.
However, a kits is not because it has no parallel sides.