Step 1: Analyze the given processes.
1. Catalytic hydrocracking: This process breaks down heavier hydrocarbons into lighter hydrocarbons like gasoline and diesel using hydrogen and catalysts. This is correct.
2. Catalytic reforming: This process converts straight-chain hydrocarbons into aromatics like benzene, toluene, and xylene, which are important petrochemical precursors. This is correct.
3. Cumene manufacture: Cumene (isopropylbenzene) is produced by the catalytic alkylation of benzene with propylene. This is correct.
4. Vinyl acetate manufacture: Vinyl acetate is manufactured by reacting ethylene, acetic acid, and oxygen over a palladium catalyst, not methane. This is incorrect.
Step 2: Evaluate the statements.
1. (1): Correct.
2. (2): Correct.
3. (3): Correct.
4. (4): Incorrect.
Step 3: Conclusion.
The correct statements are:
\[
\text{(1), (2), (3).}
\]