Is this the same sign used for 'hanging out' with friends?
No, this sign is strictly used for the physical action of hanging an object. To sign 'hang out' (as in socializing), you would use a completely different sign, typically involving both hands in 'Y' handshapes moving in small, relaxed circles.
Do I sign 'hung' differently than 'hang'?
In ASL, verbs generally do not change their form to show past tense. You use the exact same sign for 'hang' and 'hung'. To show that the action happened in the past, you simply add a time indicator like 'yesterday' or 'finish' to your sentence.
Can I change where I make the sign?
Yes! ASL is a spatial language. If you hung a picture very low on the wall, you can perform the sign lower down. If you hung a plant from the ceiling, you can reach higher up to reflect the object's actual location in your story.