Just to explain a little what it seems you are saying, first, yes, singing the prayers can certainly be a nice thing, and it helps out the actual prayers – so it’s not two separate things.
Also, about repentance for sinning, the Jewish view is that repentance isn’t simply pressing the delete button; it’s a real feeling that one really would not have wanted to make that mistake, and it was just a foolishness that came in, and that he will work on it for the future. When one has such an attitude, then it works.
The rabbis explain that since life in this world is so complex, it is impossible to go without sinning – it might even be on a superficial level – that one didn’t even realize, or a slight sin that is connected in a way to a real one. So, repentance is like taking a shower. But of course, the idea of repentance certainly doesn’t mean that one can do whatever he wants and then just repent, that is contrary to the Torah view.