Reading material: In a right triangle, the right side of 30 is equal to half of the hypotenuse. Answer the following questions according to the above materials. As shown in the figure, in the isosceles trapezoid ABCD, AD∨BC, AD=4, BC=8, point M is the midpoint of AD, and ∠ AMB = 60. The moving point P starts from B, and the moving point Q starts from C, all of which move to the end points C and M in BC direction and CM direction at the speed of 1CM/s respectively. If one of the points reaches the finish line first, the other point will also stop, and the movement time is x seconds.

(1) Judge the shape of the triangle BCM (write the answer directly) and calculate the value of X when the triangle PMQ is a right triangle.

(2) When the value of x is what, is the quadrilateral whose vertices are points P and M and points A, B, C and D a parallelogram? And write a parallelogram that meets the requirements.

(3) Is there such an x that the area of the triangle PMQ is half that of the isosceles trapezoid ABCD? If yes, find the value of x; If not, explain why.