The second question is very interesting, because the pulley is not mass, and its resultant force is zero, so the tension of the rope is 50/2=25N.

Then the rest is simple. Both objects are acted by two forces, upward rope tension, downward gravity, Newton's second law, and acceleration, okay?

The difficulty of the first problem is that the rope can't be extended, so the acceleration of two objects relative to the elevator is equal, a accelerates to the right and b accelerates downward, remember that it is the acceleration relative to the elevator.

The force of A and B are analyzed respectively, and Newton's second law is listed.

T=m_Aa_A

m_Bg-T=m_Ba_B

a_B=-a+a_A

Simultaneous solution