This can only happen if you activated iCloud on another device where no songs have been present. The app warns you that the cloud is already initialized and all local songs will be deleted. You have to confirm this warning then to enable iCloud.
The best way to restore this situation is to keep iCloud Sync enabled and then restore a full backup file. If you have not created a full backup file yet, you are out of luck. You could try to restore a full iPad backup if you have that. But apart from that there is no way to restore the deleted songs.
Regarding those files you want to delete: I don't know what files these are. If they are in the Stage Traxx folder and you have no songs in Stage Traxx, I guess you can delete them.