B, the system composed of objects and springs only uses gravity to do work, so the mechanical energy of the system is conserved, so B is correct;
C, the mechanical energy of the system is conserved, so when the object compresses the spring to the shortest, the mechanical energy remains unchanged, so C is wrong;
D, the object first makes a free-falling motion, and the acceleration decreases but the speed increases after contacting with the spring; When gravity and spring force are equal, the speed of the object reaches the maximum, so d is correct;
So choose BD.