Focal length is a measure of the lens's ability to bend light. As such this figure doesn't change when you use a smaller sensor. What actually happens when you use a smaller sensor is that your field of view narrows. Field of view is dependant both on the focal length and the format (the size of your film or sensor). The ubiquity of 35mm film among amateur photographers in the last half of the 20th century effectively took format out of the equation and lead to focal length being used to categorize the field of view.

When digital arrived and suddenly all sorts of different sensor sizes were being used the idea of a crop factor was introduced to people relate to the field of view they expected from a certain focal length on 35mm. This is not a problem so long as you realise the focal length doesn't really change, the crop factor operates only on the field of view (a crop factor of 2 halves the field of view). I agree that it would be nice to have the field if view stored in the EXIF data, seeing as the camera knows both the focal length and sensor size!

The concept of crop factors (and the term "full frame" which I avoid using at all costs) is only really used by small format photographers - no-one using medium format refers to their camera as having a 0.7 crop factor! Likewise if you were to mount a 50mm medium format lens on a 35mm sensor DSLR, it will act just like any other 50mm lens.

Similarly the minimum focus distance is a property of the lens (and distance to the sensor) and thus doesn't change when you use a different size sensor.