The correct order of density of $Be$,$Mg$,$Ca$,$Sr$ is

Consider the following reaction sequence:
$CaO + CO_2 \to A$
$A \xrightarrow{\Delta} B + CO_2$
$B + H_2O \to C$
$C + CO_2 \to D$
$D + H_2O + CO_2 \to E$
Identify compounds $D$ and $E$.

Plaster of Paris hardens by:

Heating a solid compound $X$ produces $CO_2$ gas and a residue. Adding water to this residue produces compound $Y$. Passing excess $CO_2$ gas through a solution of $Y$ produces a clear solution $Z$. Boiling $Z$ regenerates compound $X$. What is compound $X$?

Magnesia is

Chemical $A$ is used for water softening to remove temporary hardness. $A$ reacts with $Na_2CO_3$ to generate caustic soda. When $CO_2$ is bubbled through $A$,it turns cloudy. What is the chemical formula of $A$?