is it true a projection lens with longer focal length about 500mm will produce less bright image as compared to projection lens with shoter focal length about 330mm bec in longer focal length lens--500 mm- less light passes
through it ?

Not true. If the lenses are the same width, the same amount of light will pass through. The pro lens is wider (IIRC), so more light will pass through giving a brighter image. The focal length has nothing to do with the amount of light the lens passes.