How to restore my deleted songs?
There are multiple misconceptions in your "workflow", so let me try to explain them one by one:


You've copied the files to your device and placed them into a directory.
Once that was done, Android's MediaScanner found them and added them to its "library"
I've never heard they are added to the Music folder, so that might be something specific here. They were obviously not duplicated (that wouldn't make sense), so what you see as "Music folder" (you didn't specify where you checked that) is most likely rather a "virtual folder" / "Library" / "View".
As the second place was not a copy but rather a pointer, that pointer disappeared as well as soon as you deleted the file.
A "playlist" can be compared to a text-file listing up available music files, it doesn't contain the files themselves. So as you removed the files, their "pointers" were removed here as well.


So much for what has happened. Next point is that Android is not Windows (but rather based on Linux). By default, there is no "recycle bin" (though there are apps available to emulate that). Gone is gone.

For recovery (and recycle bin) you might wish to take a look at:


my listing of De-Deletion (Recovering) apps
questions tagged data-recovery
our data-recovery tag-wiki


I recommend following these links bottom-up ;)