That's a lot of questions, Tim.
1. Bit depth in the raw data
Normally (i.e. if not lossily encoded) the raw data is linear, meaning that an spot with twice the illumination of another spot is represented with twice as high pixel values an the others. The bit depth limits the number of tone levels the camera can record; however, the actual number of levels is sometimes much less than the bit depth would allow (sometimes it is a fraction of the possible levels).
2. Bit depth in the preview and in JPEG
The preview embedded in the raw file is, like the "normal" JPEG created by the camera, 8 bit per channel, i.e. 24 bit per pixel, because the pixels have three components at this stage. However, the data in the JPEG is not linear; it is adjusted to the human eye's perceptivity: we can perceive tiny differences in the dark tones, but only much larger differences in the bright region. This transformation or mapping depends on the color space, but is is (mostly) a power function, like y=x^(1/2.2) in Adobe 1998 RGB.
For example if the linear data contains 4096 levels, then the first 20 levels will be projected on 14 levels (with sRGB):
0000-0019: 000, 001, 002, 002, 003, 004, 005, 006, 006, 007, 008, 009, 009, 010, 011, 012, 012, 013, 014, 014
about 20 levels are projected to a single level in the middle of the range:
2000-2019: 186, 186, 186, 186, 186, 186, 186, 186, 186, 186, 186, 186, 186, 186, 186, 186, 186, 186, 186, 187
and the last 36 levels all will become 255.
This is often called "gamma encoding" (and some innumerates are calling the linear data "linear gamma encoded").
3. The raw conversion is between these two formats. If you are creating 16bit TIFF from the raw file, then that is usually "gamma encoded", though some converters do support linear output. The 16bit data allows higher precision resulting from interpolation/averaging. It is useful for editing and conversions, as many operations involve interpolations: resizing, curves, levels, color space conversion, free transform, sharpening, etc. I guess the majority of operations includes interpolations. Note, that at this stage we are talking about three times the bit depth per pixel.
This is a highly disputed subject, just like the merit of 14bit depth in raw vs. 12bit. I convert my raw images almost always in ProPhoto RGB, 16bit, and keep them in that form (with a few layers they can become quite large; my panos need usually many hundred megabytes in compressed form). When I create a presentation version (web or printing), then I crop, resize, sharpen, flatten, add signature, convert in sRGB, and at the very end convert it in 8bit form, for JPEG or TIFF (the latter for prints).