Borgia!
Good questions!
I'll share my research with you. Others no doubt have come to different conclusions. 1Pet.3:15.
--Did Angels who came to earth sin?
Apparently, 2Pet.2:4 says: "God did not hold back from punshing the Angels that sinned--but--throwing them into--pits--of darkness reserved for judgement.
--Did Satan when he rebeled commit sin?
Scripture says: 1John3:8. "The Devil has been sinning from the beginning--the son of man--(will)-- break up the works of the Devil", with the fulfilment of Rev.20:10.
--Why did they not die?
"One day is with Jehovah as a thousand years" 2Pet.3:8. In the day that Adam ate of the fruit he began to die. "Adam lived nine-hundred and thirty years and he died". Gen.5:5. The Devil and the wicked Angels is future. Rev.20:10.
--Why was it necessary for God to have an object or symbol of sin in the world?
The creature man, God made "according to his likeness" Gen.1:26. Obviously a higher form of life than the animals. However that would be decided by a test. How would they be different than the animal creatures? Some men would apparently "be like unreasoning animals naturally to be caught and destroyed" 2Pet.2:12.
The tree of the knowledge of good and evil would determine their willingness to follow the instruction of God. They had only one law to obey, Shouldn't have been a problem. However they chose to decide for themselves what was right and not obey Jehovah's rule of law. Gen.3:17-19.
The Sage!