Veterans with health insurance may choose to use their private health insurance to supplement their VA benefits. Payments from private health insurance usually cover copay expenses for VA health care. Having private health insurance does not affect eligibility for VA health care.
If the shape is below another, then it is always the shape above it as well. So a rhombus is always a parallelogram, a square is always a rectangle, and always a parallelogram, and always a quadrilateral, etc. If I could draw the arrows in this reply it would look better.
Not every parallelogram is a rhombus, though any parallelogram with perpendicular diagonals (the second property) is a rhombus. In general, any quadrilateral with perpendicular diagonals, one of which is a line of symmetry, is a kite. Every rhombus is a kite, and any quadrilateral that is both a kite and parallelogram is a rhombus. A rhombus is a tangential quadrilateral. That is, it has an inscribed circle that is tangent to all four sides.