Most camera's maybe. I'd be interested to see what phones write EXIF, as I would guess phone theft/loss is a more common occurrence. I tried it with my Nexus One but unfortunately it seems that it doesn't log serial numbers in the EXIF data.
Almost every modern smartphone writes EXIF - including Android and iOS.
In fact, EXIF is so common, and so poorly understood by thieves, that your only main fear is image hosts stripping EXIF, or the firmware failing to include serial in EXIF (which is less likely the more expensive the camera).
2) Seriously, do you think that a common thief cares about EXIF, let alone know?
3) I have not seen a camera which does not write EXIF -- more probable problem is that it does not write camera serial number.
4) What is the difference? You have similarly small chance of retrieving it, no matter whose possession it is in at the moment.