R.Now my questions:
1. If people misuse hung for hanged in current English, would the listener feel it jarring? Or is it still a “strict rule” people should stick to that "hanged" is used exclusively for killing someone by hanging them by the neck?
I would find it jarring. Naturally a person who would make the same mistake themselves would not find it jarring. Some people would claim that hung is as correct as hanged (but don't believe them!)
2. Could there be a possibility that hung is used for someone, meaning not to kill him but just to hang him up as in:
Pictures are hung on the wall. (I know this is correct.)
He was hung on the tree. (What about this sentence? Is there such a possibility of using "hung" to mean "hanging him up for a while"?
Yes, there is. But it will be misunderstood unless you make it clear that he was simply hung there for a while but not hanged.