How do I work in 16-bit color in GIMP, and can I save 10-bit files?

You can use the 0..100 scale:

This is a percentage with one decimal digit, so in high precision modes, it is mapped to 1000 different values, and therefore about 10 bits.

To edit in 16-bit set the image to a high precision mode (Image > Precision). Technically, there is no point in using 16-bit precision in Gimp unless you are very RAM-constrained. The Gimp engine works with 32-bit floating point values that are even more fine-grained, so if the image is 32-bit FP linear, you skip conversions.

When you save the image as XCF, if it of course saved with its current precision.

When you export to other formats, it depends on the format but I don't known of any 10-bit formats, it's usually 8-bit/16-bit integer or 16/32-bit FP.

• When exporting to PNG Gimp uses PNG16 by default if the image is in high precision (anything but 8-bit).
• When exporting to TIFF it uses the relevant TIFF variant: 8/16/32 bits (at least as long as you don't use JPEG compression).

IMHO the accuracy of the color isn't what is important (I sincerely doubt that between your camera, the display, the lighting conditions, you can be accurate to 10-bit). High-precision is more about giving more intermediate values and avoiding round-off errors.

Edit: Complement: the single decimal digit in the color selector is an arbitrary limit for the UI. In the Python console, try this:

>>> import gimpcolor
>>> gimp.get_foreground()
gimpcolor.RGB(0.0, 0.0, 0.0, 1.0)
>>> gimp.set_foreground(gimpcolor.RGB(0.12345678,0.98765432,0.23456789))
>>> gimp.get_foreground()
gimpcolor.RGB(0.12345678, 0.98765432, 0.23456789, 1.0)

The 0% ➜ 100% values in the color selector are really 0.0 ➜ 1.0 values for Gimp. The 4th number is the alpha channel. The above shows that Gimp can use fore fine-grained values. Try yourself with other values, but see if you can spot a difference between two colors that differ only by the 5th digit in a high-precision image.