Although waves produced on the sea can cause different points of the sea surface to reflect sunlight towards the same observer, how is that kind of ribbon image produced? Why isn't the reflection stretched also perpendicularly to the line of sight by wavyness of the sea?
First off, some terminology: the 'ribbon' is known as sun glitter (and, when observed from space, as sunglint). A good explanation is at this NOAA page, but the basic dynamics is that the light reflects specularly off of the water, but the variable angles of the surface deflects it in different directions.
If you were to see the sun glitter at normal incidence (i.e. the Sun at the zenith, observed from above the water, either from a plane or from space) then it would look completely round. As the elevation of the Sun decreases and it moves from the zenith to the horizon, the glitter becomes more and more elliptical, until it becomes a ribbon as in your image.
On the other hand, if the water were completely still, with a smooth and horizontal surface, then the sun glitter ribbon would be gone, and you would just see a direct mirror image of the Sun.
Yes, the image of the sun or moon in a perfectly flat lake or ocean would be round. The "ribbon" is due to ripples in the surface of the water. To understand why it's a ribbon instead of a broad expanse of reflected light, all you need to do is shine a flashlight, at the top section of a reflective ball, move the laser in a small circle parallel to itself, and see where the reflected light goes. It's spread into a beam that lies in a vertical plane. The "parallel to itself" requirement is to make sure you're simulating a collimated beam. You can accomplish the same thing by forming a collimated beam using a telescope.
