<image>(2016 Spring • End of term in Guanyun County) As shown in the figure, extend side DC of the parallelogram ABCD to point E, so that CE=DC. Connect AE, intersect BC at point F, and connect AC and BE.
(1) You determine the shape of quadrilateral ABEC is ____;
(2) Please add one condition to make quadrilateral ABEC a rectangle, and please explain why;
(3) When △ABC meets the ____ condition, quadrilateral ABEC is a rhombus. (No need to explain)