Step 1: Analyze reactivity with water.
Lithium and magnesium both react slowly with water, unlike other alkali and alkaline earth metals.
So, Statement I is correct.
Step 2: Nature of bicarbonates.
Lithium bicarbonate does not exist as a solid under normal conditions, and magnesium bicarbonate is only stable in aqueous solution.
So, Statement II is incorrect.
Step 3: Solubility of chlorides in ethanol.
Lithium chloride is soluble in ethanol, and magnesium chloride also shows moderate solubility.
So, Statement III is incorrect.
Step 4: Thermal decomposition of nitrates.
Both lithium and magnesium nitrates decompose on heating to give respective oxides, NO2, and O2.
So, Statement IV is correct.
Hence, only Statements I and IV are correct.