The focal length doesn't change. A 10mm focal length lens is always a 10mm focal length lens. It's just that on a crop sensor, ie smaller than a full frame sensor, doesn't collect the same area of light, so the apparent field of view is narrower by whatever fraction of a full frame sensor it is (1.6x for APS-C). But it's still 10mm focal length.
http://www.bobatkins.com/photography...nd_lenses.html
F-ratio is not affected.
Depth of field is subtly affected, because it's a function primarily of f-ratio and distance to subject, but also circle of confusion, sensors etc do come into it.