Answer to Question 1
Sodium chloride and bromide are very soluble in water. If there is too much water present, these products do not precipitate and it is not possible to evaluate the relative rates of reaction.
Answer to Question 2
Acetic acid, a carboxylic acid, has a very similar pKa to the carboxy group of naproxen. Using only one equivalent of acetic acid to neutralize sodium naproxen would result in a Keq of about 1. Therefore, in order to fully protonate naproxen with acetic acid, we would have to use a large excess of this material. On the other hand, sulfuric acid is a much stronger acid than a carboxylic acid and will fully protonate a carboxylate with only one equivalent.
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