With cameras and their lenses, an iris diaphragm is used to control the amount of light that hits the film or chip. That is, the diaphragm opens or closes to varying amount, thus giving you one way to control the exposure. The other way is to vary the shutter speed.
Another factor controlled by the iris (aperture) is the depth of field.
The larger the F number, the smaller the diaphragm opening and the less light let through to the shutter and film or chip. Also, the larger the F number, the larger the depth of field.
The focal length and design of the lens determines the field of view. The F number has nothing to do with the field of view.
With telescopes, the F number has nothing to do with the amount of light coming through the scope because there is no iris diaphragm. The F number is simply the ratio of the scope's aperture and focal length.
If you have an 8" F5 telescope and a 12" F5 telescope, the 12" telescope's aperture is much larger and lets in more light. They both, however, have the same inherent F number and field of view. When you put an eyepiece into the equation, however, its design will determine the usable field of view at a given focal length.
Zoom camera lenses are like eyepieces in that they control the magnification and the field of view. A similar effect occurs with digital zooms in electronic cameras ... when you zoom "up" in power you gain magnification and lose field of view.
Don't confuse this will manually changing the aperture (F number). All that does is change the amount of light coming through to the film or chip, and change the depth of field (focus) of the shot.
Think of it this way: The F number is just a number on the camera dial to give you a reference point. While it's true it has a mathematical basis and is linked to exposure and depth of field as physical parameters, it really is nothing more than an indicator.
Nothing "draws light quicker". A larger aperture lets in more light (but at the same rate as a smaller aperture).
It is not a waste of time to attempt -- even to fail -- at taking astrophotographs at 3/4 Moon, as long as you learn something. If your target is very near the Moon in the sky at the time, you may get glare or internal light path reflections, however.