Focal length can be cumbersome to define, witness the
Wikipedia article. For a single element it's pretty straightforward, but camera lenses are not single elements, so the focal length is a function of the combinations of elements. It really has nothing to do with any physical measurement in the camera or lens. Generally, a bigger number is more magnification, a narrow field of view, what we call telefoto. A smaller number is less magnification, a wider field of view, what we call wide angle.
What focal length lens falls into these categories depends on the size of the image created in the camera. That's the frame size on the film, or the sensor size in digitals. A 50mm setting would be extreme telephoto on a cheap point-and-shoot digital, but a wide angle lens on a medium-format camera. Most of us think in terms of the 35mm world, though.
An effect of the focal length is the perception of perspective. A longer lens will flatten the perspective of the view since its view is so narrow. A wide lens will exaggerate the perspective since it's cramming such a wide view onto the frame. We see that as distortion in the image, things stretched out in the corners, curved on the sides, etc. A lens which yields an image whose perspective is comparable to what we see with the naked eye would be called a "normal" lens. In the 35mm film world, that's a 50mm lens, which is why the kits used to come with just that one lens. Most digital SLRs, it's probably a 35mm or so. In point-and-shoots, it's an incredibly small number. My Sony Cybershot has an 8-24mm zoom on it. (That tells you something about the sensor size, since the 24mm is actually quite strongly telephoto on this camera.)
Basically, you could call anything longer than normal a telephoto. You could call anything shorter than normal a wide angle.
The next question is "why non-zoom lenses anyway?" If you can carry a couple of zooms, say an 24-70 and a 55-200, why would you want anything else?
Two answers. First, speed. Zoom lenses are ALWAYS slower than fixed-length lenses, unless you've got thousands to spend. I have a 50mm f1.4 lens on my Nikon n8008, and I have a 70-200 zoom that's f-4 at 70mm and only f-5.6 at 200mm. If it gets dark and I need the longer lens, I have to switch to fast film or a tripod, because I'll need longer shutter speeds to get enough light.
Second answer is distortion. Zooms are way better these days than they were when I started in the 70's. A zoom lens would usually have terrible barrel distortion as it went through its range. One end everything at the edges curves inward, at the other end everything curves outward. Purists always scoffed at anybody that showed up with a zoom lens. They were too poor to get enough "real glass" to cover their needs.
Another problem with zooms is control. Some lenses have a separate ring for focus and zoom, some combine both functions on one ring. When you're shooting fast, like an airshow or a race, you really really want the 1-ring zoom. It's a royal pain to switch between controls to set zoom length and then focus before the subject is passed out of view.
As for your exposure question, there's always a "correct" exposure that brings the correct amount of light onto the film or sensor. That correct amount can be balanced by changing f-stop and shutter speed. If 1/125-second at f-4 is correct, then so is 1/250-second at f-2.8, or 1/1000-second at f-1.4. The first setting might have a little motion blur, the last one would be frozen but have a very shallow depth of field. Which one is correct? All are, for exposure, but for the desired effect, it depends on what you want.
In your first post you asked about numbers on the lens. Since then I found this image on Wikipedia, in the article on
exposure.
You see a window near the front of the lens, a scale right under that, and a scale near where the lens attaches to the camera. This is a non-zoom lens, so there's no scale for focal length.
The window shows the distance the lens is focused for. Look through the viewfinder, focus the subject. 99% of the time you could care less what's in this little window.
But, if you want to know the correct f-stop for a desired depth of field, that's what the scale under the window is for. The thick line in the center is the distance to the subject, in this case about 1-1/2 meters. You see the lines pointing to 11 on either side of that, lined up at about 1 and 2 meters. That tells you that at f-11, the distance range from 1 meter to 2 meters will be in focus. at f-16 a little bit more distance is in focus, and at f-22 quite a bit more, just about all the way to infinity. You don't see markings for smaller f-stop numbers, they are too close to each other to worry about, but you could judge pretty well by guesstimating that at f-4, you might only have 3 or 4 inches of focus depth.
That scale exists on a zoom lens as well, but as a set of curved lines. You read it at the end of the zoom barrel.
Notice the little white dot under the focus window. That's for infrared film. If you shoot infrared, you have to adjust the focus, because infrared light bends differently than visible light as it goes through the lens. Basically, focus through the viewfinder, then move the focus so the point at the heavy line moves to the dot. That compensates for the infrared difference.
Finally, the numbers at the base of the lens are, of course, the manual settings for aperture. The 22 is red because that's where you put it for automatic aperture. Turn the ring to put the f-stop you want next to the white dot above the ring.
At the side, the 35mm 1:2 tells you that this lens has a focal length of 35mm, and a maximum aperture of f-2. The D is what model series it is in Nikon's line. This is a fixed-length "normal" lens for their digial SLRs.
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