1. Statement I: Lithium halides (e.g., LiCl) have covalent character due to Li$^+$'s high charge density (Fajans' rule), making I correct. 
2. Statement II: NaNO$_3$ decomposes on heating to NaNO$_2$ + O$_2$, not NO$_2$, so II is incorrect. 
3. Statement III: LiHCO$_3$ is not stable as a solid; it exists in aqueous solution, unlike other alkali bicarbonates, so III is incorrect. 
4. Statement IV: Only Li, Na, K form ethynides (e.g., Li$_2$C$_2$) with ethyne; Rb, Cs do not, so IV is incorrect. 
5. Thus, only I is correct, so the answer is (3) I only.