The first question is true, because AB=BC and angle BAD = 90, so angle BAC = 45, so we can get angle BAC = angle DAC = 45, which can be verified according to the edge theorem.

The second problem is that the triangle cCDE is equilateral, because the angle BCE= 15, so the angle ACE=30, and because the two triangles are congruent, so the angle DCE = 60, so the triangle CDE is equilateral;

The third question, EH=2BE, let AE=x, AB=y, and the angle AHE is a right angle of 30 degrees. Looking for a relationship, you can find that this problem is not established; In the same way, we can also find that the fourth question is not valid.