When the coconuts run out, will my villagers go back to fishing until the access to another food source is finished? In VV1, I constantly had villagers dying of starvation cos they wouldn't forage for berries when the crops ran out, even if the berry bush had berries on it. Will these villagers fish on their own when they run out of coconuts, or will I have to manually make them fish?

It depend, which is your level of Farming?

It really sort of depends on if you have the (highlight for spoiler) algae in the ocean yet. If you do, you need some other tech and stuff to make them fish again. But usually they will go back to fishing.

I have the second level of farming, and no algae yet, cos I didn't fish much before getting access to the coconuts. They didn't start fishing on their own after the coconuts ran out, but once I dragged my two farmers into the ocean, they seem to be continuing to fish for themselves. So, I should be ok until I get the dam built and they can use that for food!