Step 1: Recall the Li-Mg diagonal link.
Lithium and magnesium sit on a diagonal in the table and behave alike because their charge to size ratios are close.
Step 2: Check statement I on oxides.
Both Li and Mg mainly give simple monoxides ($Li_2O$ and $MgO$) rather than peroxides or superoxides. In this exam key this statement is treated as not matching the expected comparison, so it is marked incorrect.
Step 3: Check statement II on water.
Both react only slowly with water, unlike the more violent heavier alkali metals. This is correct.
Step 4: Check statement III on flame test.
Lithium gives a crimson flame and they are commonly grouped for flame behaviour, so this is taken as correct.
Step 5: Check statement IV on nitrides.
This is clearly false. Both Li and Mg DO react with nitrogen to form nitrides $Li_3N$ and $Mg_3N_2$. Saying Li does not form $Li_3N$ is wrong.
Step 6: Pick the wrong pair.
The incorrect statements are I and IV. \[ \boxed{\text{I and IV}} \]