The farmer IS in the boat. (Meaning he is riding in the boat)

I've never heard that expression and I couldn't find it online. It sounds like an idiom, but since I found no examples of it, perhaps it has more to do with the context you found it in. If I had to make a guess, I would say that it's a metaphor for someone being out of their natural element.

I think that kind of Idioms

In English, we use sometimes smash words together. "Is" is one of the words we like to do this with. So, as in your example, "The farmer IS in the boat" becomes "The farmer's in the boat". We crush "farmer" and "is" together, connecting them with a little apostrophe to make "farmer's".