Yes. A rhombus has four sides, qualifying it as a quadrilateral. Rhombuses also have four congruent (equal) sides.
No , a quadrilateral has four congruent sides. The top , bottom , and two sides.
An impossibility. By definition a quadrilateral with 4 congruent sides must have congruent adjacent angles.
A quadrilateral with four congruent sides and uncongruent diagonals is a Rhombus. See related link for a picture
trapezoid * * * * * It cannot be a trapezoid because that does not have four congruent sides. In fact it need not have even two congruent sides. The correct answer is a rhombus.
It is a square.