3. What I don't understand is how mapping 16-235 to 0-255 doesn't increase contrast ratio.
Let me see if I can explain this clearly. There are few different considerations involved.
The first is the dynamic range of the content itself. Studio levels(nominal 16-235) has increased dynamic range over PC levels(0-255), while also ever slightly less bit depth within the reference range. This may seem counterintuitive because the numerical range is larger with PC levels. So keep in mind that the dynamic range of the content itself is slightly greater with Studio levels.
Regardless, the next consideration is how to display the ranges. We want black to be black on the display, obviously. This is a simplificationi, but I'll move on from that. But what should white be? On a CRT there isn't a hard clip point, so it's not really a problem. We set white to a bright enough level, and we enjoy our image. With digital displays our contrast range via the display is very low, and we have these relatively hard clip points including for white. We have very different aims when calibrating. When setting white on a digital display if you don't maximize the limited CR capability of the display you're not getting as good an image as you can. Now you see that we have a problem that we did not previously have to consider whith CRT which doesn't really have a maximum white point at all and doesn't have a limited CR range that you're trying to maximize (since it's essentially infinite).
Do you choose to align peak white of the display to peak white of the content, which would be 254? This would be technically correct and maintain all video content.
Do you choose instead to boost white level beyond that and say choose to align the display's peak white to the content's reference white which would be 235? Now we're clipping or colorshifting peak whites that may be present and that may or may not be significant. But we're getting better CR performance out of our display.
Do we choose come other compromise point?
These are decisions that each user encountering this compromise should make on their own. The more severely you cut into the video content, the more likely visibly negative consequences will result. This will depend partly on the specific content, and also your pickiness and preferences. But basically yes, the more whites you clip off yes you are expanding the contrast in the parts of the image that are left. Of course, a good argument can be made that this is a very worthy compromise if done conservatively and with purpose and awareness.
Now, remember that this is different than just remapping 16-235 to 0-255. Doing that won't provide any contrast ratio advantages that you couldn't achieve by simply aligning the display to 16-235 in the first place. But you do force the choice and decrease the content's dynamic range, and also may likely end up suffering banding problems (though so many systems have such terrible banding problems it may not be a particular concern).
2. I also understand that on an 8-bit display that banding can occur, but I have a 10-bit display so this should be less of an issue if it is one at all.
Remember that uunless you have a way to feed that display higher bit-depth (i.e. not DVI or RGB via HDMI), then you are going to run into banding problems because there is an 8-bit bottleneck there.
Actually both ChrisWiggles and stacey spears agree that using 0-255 instead of 16-235 on a digital display like an LCD would increase contrast ratio.
I agree, but to be clear this is aligning the display to 16-235 instead of 16-254. I do not advocate re-mapping the range to 0-255 and then aligning to 0-255. And the same statement can also be taken to an illogical extreme. The more you raise your white level, the greater contrast you're going to get for what's left. Does this mean that it's a good idea to turn up your white level to the absolute maximum? Of course not. The point is to get the best and most accurate image possible overall, and with a digital display with limited on/off CR range and hard clip points this involves some compromises.