I got to level 2 farming. How long will it be until the crops produce food? Do I need level 3 for them to grow? If so, am I wasting my farmers time by letting him water them at level 2?

They'll grow at level 2, but you don't need anyone to water or plant, just put the farmers doing something else, like researching, until the crops come in. You can check the time left by clicking on the farm.