A, after the electric field is applied, the ball A is forced by the electric field to the left and the ball B is forced by the electric field to the right. The electric field force does positive work, the potential energy decreases, and A is wrong;

B. After the electric field is applied, the ball A is subjected to the left electric field force, and the ball B is subjected to the right electric field force. The electric field forces on the two spheres are equal in magnitude and opposite in direction, and the resultant force is zero, so the momentum of the system is conserved. Therefore, B is correct.

C, when the spring length reaches the maximum, the electric field force does the most work and the electric potential energy drops the most, so the mechanical energy of the system is the largest, so C is wrong;

D, two balls away from the process, first do the acceleration movement with decreasing acceleration, and then do the deceleration movement with increasing acceleration. Therefore, when the electric field force and elasticity are balanced, the acceleration is zero and the kinetic energy is the largest, so d is correct;

So choose BD.