Step 1: Recall that a unit hydrograph (UH) is built on assumptions of linear response and uniform rainfall excess over the catchment.
Step 2: Check (C): the actual textbook limitation is that a $\text{non-uniform}$ precipitation spoils the UH results, not a uniform one, so as printed, (C) is wrong.
Step 3: Check (E): the accepted guideline links the rainfall duration to a fraction of the basin lag different from $1/6$ to $1/2$, so (E) does not hold either.
Step 4: That leaves (A), (B) and (D), all of which describe genuine restrictions of UH theory: no snow melt representation, no large surface storages, and constant rainfall intensity over the excess duration.
\[\boxed{\text{Answer: (A), (B) and (D) only}}\]