To me, forgetting all religious overtones, repentance means someone recognizes that what he has done was wrong in some way, he recognizes he ought not to do wrong and sets out to not do those things he sees as wrong in the future. It might also involve him trying to make amends with anyone he's harmed.
HOW he determines what is wrong IMHO is through a combination of listening to his instincts, considering what his society deems right/wrong AND overlaying that with reasonable application of empathy. Is it fool proof? No. But other than that, I know of no way someone will recognize right from wrong. I believe humans, along with some other higher animals, evolved with some sense of right and wrong within the confines of their species. IOW, what is 'right' for a lion, ie a male lion slaughtering the offspring from some other male lion, would be deemed horrific to humans. But that's THEIR kind of morality, for want of a better word. And lions live by THAT code...it is how they survived and thrive. Humans, I believe survive and thrive living by other kinds of codes which most likely involve the things that comprise our codes/laws/norms.
No...one person cannot bear the sins of another. I don't care what a god might say, it is simply an impossibility. Even if a god says that's the way it must be, said god is wrong and it's nonsense.
NOW, a capricious god might look at the world and decide that this or that action is a 'sin' and then decide that all those sins are somehow no longer too bad to forgive because some entity suffered, but that's just an arbitrary whim on the part of that god. He could likewise say the suffering of an entire people...ie the Jews, can likewise somehow make it easier for him to save humanity from sin whether the Bible says that's what happened or not. Or, a god could say that by making all the water on an uninhabited planet boil is how he deals with sin and it would be just as effective.
But in the end, regardless of what a god says, one is still responsible for the wrongs they commit against their fellowman and the degree to which they are ever forgiven is entirely UP TO the wronged party, A person can forgive themselves for their past deeds and...that's one way to deal with guilt. But that is irrelevant from the point of view of another, wronged party.