Step 1: Understanding the Statements.
- Option (A): Grain size in a deltaic succession typically coarsens upward due to the change in energy conditions. The lower layers are finer, while the upper layers are coarser as the water velocity increases. This is a correct statement.
- Option (B): Paraconformity is an unconformity that lacks a distinct erosional surface, so this statement is incorrect.
- Option (C): The Paleogene Period indeed includes the Paleocene, Eocene, and Oligocene epochs. This is a correct statement.
- Option (D): A sea-level fall typically causes the river mouth to shift landward, not towards the deep ocean. Hence, this statement is incorrect.
Thus, the correct answer is (A) and (C).
Final Answer:
\[
\boxed{(A), (C)}
\]