Hung may not be "incorrect" (as a substitute for hanged), but it is certainly ambiguous.

A hanged person is one who was killed by hanging. But a hung person may still be alive after merely having been been suspended for a while.

I thnk I can answer two of your questions Mary.

Q: You said "I think there is a time to use hung and there is a time to use hanged but I just don’t know when to use either one."
A: As I understand it, you have been hung if you are taken down still alive. If you die by hanging, then you have been hanged. Also, objects cannot undergo death by hanging, so are alway hung and not hanged. Btw, Reagan was correct to use "hung" when he said "I'll be hung in effigy" -- since an effigy is not alive, it can be hung but not hanged.

Q: You asked "But what about sung instead of singed?"
A: Sung is the past tense of sing -- "A song was sung" or "I sung a song". But singed is not the past tense of sing -- "When he got too close to the fire, he singed his eyebrows." or "Her hair was singed by the curling iron."

I agree with caes ---
"caes says:
October 14, 2009 at 3:03 pm
hanged is used when talking about people being hanged (killed by hanging). in other cases, you use hung."

As I understand it, you have been hung if you are taken down still alive. If you die by hanging, then you have been hanged.

So "hung, drawn and quartered" meant being taken down alive so you could suffer the additional punishment of being gutted and chopped into pieces.

Objects cannot undergo death by hanging, so are alway hung and not hanged.

So, "He was hanged" means he is now dead, but "He was hung" leaves the question open.