(i) If velocity of bock A is zero, from conversation of momentum, speed of block B is 2u. Then KE of block $B=\frac{1}{2}m{\left(2u\right)}^2=2m{u}^2$  is greater then net mechanical energy of the system. Since this is not possible, velocity of A can never be zero.

(ii) Since initial velocity of B is zero, it shall b zero for many other instant of time.

(iii) Since momentum of system is non-zero, KE of system cannot be zero. Also KE of system is minimum at maximum extension of the spring.

(iv) The potential energy of spring shall be zero whenever it comes to natural length, Also PE of spring is maximum at maximum extension of the spring.