Step 1: Analyze the given reaction conditions.
- Reaction (i): Phenol reacts with sodium hydroxide and hydrogen ion to form phenoxide. This matches \( P_1 \) as Phenol.
- Reaction (ii): Phenol undergoes a Kolbe reaction with sodium hydroxide and carbon dioxide, resulting in the formation of salicylic acid. So, \( P_2 \) is Salicylic acid.
- Reaction (iii): The reaction with sodium hydroxide and methyl chloride suggests a methylation, leading to the formation of anisole (phenyl methyl ether). Therefore, \( P_3 \) is Anisole.
- Reaction (iv): Phenylacetate reacts with sodium hydroxide and carbon dioxide, which forms aspirin (acetylsalicylic acid). Hence, \( P_4 \) is Aspirin.
Step 2: Write the correct product names based on reactions.
Thus, the final products are:
\[
P_1 = \text{Phenol}, P_2 = \text{Salicylic acid}, P_3 = \text{Anisole}, P_4 = \text{Aspirin}
\]
Step 3: Final conclusion.
Therefore, the correct sequence is option (3):
\[
\boxed{P_1 = \text{Phenol}, P_2 = \text{Salicylic acid}, P_3 = \text{Anisole}, P_4 = \text{Aspirin}}
\]
So, the correct answer is:
\[
\boxed{(3)}
\]