does directors and producers have great knowledge on photography?

Remember that the director is the head of the production of the movie and are hired because of their expertise and capability of handling all the aspects of the film. Since Cinematography is a significant element of a movie, Directors require knowledge of photography simply because movies are still pictures, moving pictures to be exact. The aperture, ISO,frame rate, aspect ratios and resolutions, shutter speed, depth of field, all of those elements are found in motion picture cameras and directors are familiar with this because it's an integral part of the vision for the film. Of course no one is as good with this as the Director of Photogaphy who handles the lighting, framing, camera movement and overall LOOK of the film with the help of the cinematographers of course. Say if you were watching a horror film, the director of photography is the one responsible for getting that artistic dark tone of the scenes.

Producers on the other hand, probably are familiar but they focus more on hiring the crew members, director, actors, writers, handling the financial negotiations (exec. Producer). Basically bringing everyone in the movie together is what the producer is in charge of. Unless you're working with an experienced director and producer like Steven Spielberg, he has great knowledge of photography.

So yes, directors (directors of photography/cinematographers especially) should be and are very knowledgable with photography. The big difference is that camera movement and visual storytelling is something filmmakers are more adept with than photographers.

It is a team work. There are cinematographers to realise the vision of directors.