I) Stability of superoxides increases down the group due to increase in cation size which stabilizes the larger anion O$_2^-$ better. Hence, NaO$_2 < KO$_2 < RbO$_2 < CsO$_2$ is correct.
II) Basic strength of group 2 hydroxides increases down the group due to increase in ionic character and solubility: Mg(OH)$_2 < Ca(OH)$_2 < Sr(OH)$_2$.
III) Thermal stability of carbonates also increases down the group due to increased lattice energy stability: MgCO$_3 < CaCO$_3 < SrCO$_3$.