Does my statistics affect my harpooner?

Yes, the higher your stats are in a particular element, the more damage the harpooner will do in that element. With the new Harpooner mechanic, i.e. you don't have to arm it as it automatically picks the best element, it should be mostly using whatever element(s) match with your stats based on the target.

Yes, as MrDSire#5734 said, the harpooner automatically chooses the most damage you can deal. Every 10 stats, 1 damage.