1: Yes, it's fine. It's not common, but it's OK. 2: It is possibly implied, but it isn't stated explicitly. 3: No, they are similar, and the difference is probably just what fitted the rhythm of the song. I not sure I understand what the person who made a comment said, but the bit about crossing the doorstep is wrong. If anything, the 'on' suggests that coming might take some time - extending the idea of a continuous tense. 4: It's not clear. Perhaps he made a mistake? Perhaps she did, and she realised that. The point of the song is that she is giving him another chance.

1) it's not correct, but it's a creative way to make a song sounds better to listeners. 2) According to the original lyrics: Since you left me, I'm so alone Now you're coming, you're coming on home I'll be good like I know I should You're coming home, you're coming home She left the main character, but we can't definately say that everything is over between them. probably their break is his fault, because he wants to be better than he was before. 3) there is no strong difference between the meanings. "you're coming home" means that she will come BACK home (in general) "you're coming on home"* means that she will definately cross the doorstep (real action from her in real time) *according to the Oxford Dictionary: "come on" usually used in the progressive tenses (of an illness or a mood) to begin