1) Not imbedded in the image
2) Included with the post information when a site's EULA states it will be public information
3) Normally kept private on social media sites to prevent stalking
4) Usually only made available to a requesting party via court ordered subpoena because of #3
If you suspect the image is of an illegal nature and want to report it, you can contact the hosting ISP and also a number of reporting channels from local and federal law enforcement and investigative groups.