Correct options are A) and C)

Solubility of alkaline earth metal's thiosulphate decreases down the group.

The difference in lattice energy and hydration energy decreases on moving down the group.

Thus, the option A is correct and the option B is incorrect.

Solubility of alkaline metal's carbonate increases down the group. The difference in lattice energy and hydration energy increases on moving down the group.

Thus, the option C is correct and the option D is incorrect.