I suppose it is not impossible. Houdini the famous escape artist apparently had some weird ability to dislocate his arm or shoulder or something, which helped in his abilities to escape the straight jacket. For the rest of us "normal" folks, IF such a thing is possible, I would imagine the process to be a little on the painful side.
Usually not unless it is only slightly offset, if it is completely out of socket you really should have a health care professional do it, it takes a lot of force to get them back in generally and if you aren't careful you can injure it worse.
I used to hold my hands together and go over my head, all the way around to my lower back. My Left shoulder popped out a few times. I would bend forward and shake my arm, it would go back in, but it hurt for awhile.