Step 1: We want the incorrect statements.
Check each one and mark whether it is right or wrong.
Step 2: Statement-I.
Water ionises more as temperature rises, so at $310\,K$ the value $K_w$ is larger than at $298\,K$. That makes neutral pH a little below $7$. So Statement-I is correct.
Step 3: Statement-II.
For very dilute $10^{-8}\,M$ HCl, the $H^+$ from water cannot be ignored. Adding acid can never make a solution basic, so the pH stays just below $7$, around $6.96$, not $8$. So Statement-II is incorrect.
Step 4: Statement-III.
$CH_3COONa$ is a strong electrolyte and is almost fully ionised. Acetic acid only suppresses the ionisation of the acid through the common ion effect, not the ionisation of the salt. So Statement-III is incorrect.
Step 5: Statement-IV.
CuS has a much smaller $K_{sp}$ than ZnS, so in acidic medium only CuS precipitates while $Zn^{2+}$ stays in solution. So Statement-IV is correct.
Step 6: Collect the wrong ones.
The incorrect statements are II and III.
\[ \boxed{\text{II, III}} \]