Carbonates and sulphates of lithium decompose on heating while the stability of carbonates and sulphates of other metals increases down the group.

No explanation is given for this question. Let's discuss the answer together.

Alkali metals have the lowest ionisation enthalpy in each period because alkali metals are largest in their respective periods and therefore, the valency electrons are loosely held by the nucleus.

Sodium is prepared by electrolysis of molten $$NaCl$$  as
\[\begin{align} & 2NaCl\xrightarrow{\text{Electrolysis}}2Na+C{{l}_{2}} \\ & \text{At cathode:}\,\,2C{{l}^{-}}+2{{e}^{-}}\to C{{l}_{2}} \\ & \text{At anode:}\,\,\,\,\,\,2Na\to 2N{{a}^{+}}+2{{e}^{-}} \\ \end{align}\]

A mixture of $$N{a_2}C{O_3}$$   and $${K_2}C{O_3}$$   is used as a fusion mixture.

$${\text{Alkaline earth metals}} - $$
\[M-1{{e}^{-}}\xrightarrow{I{{E}_{1}}}\underset{n{{s}^{1}}}{\mathop{{{M}^{+}}}}\,\xrightarrow[-1{{e}^{-}}]{I{{E}_{2}}}\]       \[\underset{\left( \text{Noble gas configuration} \right)}{\mathop{{{M}^{2+}}}}\,\]
$${\text{Alkali metals}}{\text{.}}$$
\[\underset{n{{s}^{1}}}{\mathop{M}}\,-1{{e}^{-}}\xrightarrow{I{{E}_{1}}}\underset{\left( \text{Noble gas configuration} \right)}{\mathop{{{M}^{+}}}}\,\]       \[\xrightarrow[-1{{e}^{-}}]{I{{E}_{2}}}{{M}^{2+}};I{{E}_{2}}>>I{{E}_{1}}\]

As ionisation energy decreases from $$Li$$  to $$Cs,$$  electropositive character increases from $$Li$$  to $$Cs.$$

Large amount of hydration energy makes it strongest reducing agent inspite of its highest ionisation enthalpy.
\[{{M}_{\left( s \right)}}\xrightarrow[\text{energy}]{\text{Sublimation}}{{M}_{\left( g \right)}}\xrightarrow[\text{energy}]{\text{Ionisation}}\]       \[M_{\left( g \right)}^{+}\xrightarrow[\text{energy}]{\text{Hydntion}}M_{\left( aq \right)}^{+}\]

Electrons in $$Mg$$  due to its small size are tightly bound so they cannot be excited by the flame.

Key concept More the extent of hydration, lesser is the ionic mobility.
In all the alkali metals, $$L{i^ + }\,ion$$   is smallest. Thus, extent of hydration is maximum in $$L{i^ + }\,ion.$$
i.e. the dissolution of $$L{i^ + }$$  in water occurs and get hydrated. Smaller the size of a cation, greater is the extent of hydration and lesser is the ionic mobility.