Slice Geometry generates a histogram from the stack’s pixels then applies ImageJ’s ‘default’ threshold to it. The result should be the same or similar to what you get from the Image > Adjust > Threshold command, checking ‘Stack histogram’ and selecting ‘Default’ from the Autothreshold menu.
The code which does it is here and here and here. The histogram utility methods predate ImageJ having an inbuilt stack histogram method, so are a bit redundant these days.
If your images are Hounsfield Unit (HU) calibrated (as many clinical CT images are), Slice Geometry will attempt to detect it and set the min to 0 HU (water, partial bone pixel) and max to 4000 HU (bit more than cortical bone, less than steel).
Yes, if your images are all very similar or HU calibrated. The min and max are sensible suggestions based on our typical use case, but are potentially inappropriate for your images. The best way to check is to see whether the min and max values agree with what you would have chosen, and to do a sensitivity analysis to see how varying them alters your results.
Slice Geometry has a new feature (since BoneJ 1.4.2) which allows you to incorporate partial pixels, so if your pixel is 0.3× the value of a fully dense one, offset a bit for the surrounding air, you can add an 0.3× pixel to the area and second moment of area measurements. It’s described in more detail in the preprint which stimulated its development.