Yes: ∠DBC=∠A/2

2: CE is the midline on the hypotenuse AB, so CE=AB/2 AB=2AC, so CE=AC.

Because AB=2AC, ∠B=30 ∠A=60, the triangle ACE is an equilateral triangle, and CD is high, so CD is also an angular bisector, so ∠ECD=30.