First the original files where accidently deleted. Out of that, recuva created new information data. The deleted originally data is overwritten by the new recuva data, So the deleted originally data cannot be used for recreating anymore. Is it possible, to recreate the original files only by the new recuva information data?
Recuva does not "create" data, it just recovers what is already there.
Are you saying that you wrote the recovered data back to the drive that you were recovering from?
That is something that you should NEVER do, it can/will overwrite what you are trying to recover before it has been recovered. You should always recover to a DIFFERENT DRIVE. (It does warn you about that when recovering).
If you have recivered back to the original drive then the original data is now probably lost for good.
You could try running Recuca again and saving anything that it might recover to a DIFFERENT DRIVE but I wouldn't hold out too much hope now.