Today when I startet my computer and mounted the partition with VeraCrypt it accepts the password but the new drive (X:) shows no info like a unallocated partition and windows wants to format it.
When you used the Select Device button and selected the partition that is encrypted, what drive letter in VeraCrypt was selected? X or R? Since you can mount the partition using drive letter X, the drive letter being assigned is what you selected in the VeraCrypt
main program. You may not have realized that it was mounting to X when you meant to mount to R drive letter.
When the encrypted partition is unmounted, make sure Windows does not have a drive letter already assigned to the unmounted encrypted partition. Use the Disk Management for the unmounted volume from Windows using the Change Drive Letter, then Remove.
Is there a way to decrypt this NON-SYSTEM partition like a common VC system partition?
Currently not possible. A request has been created to allow in-place decryption of non-system drives/partitions. You can vote-up the request at the link below.
I backed up the headers and everything but can't find an option.
Since you can already mount the volume successfully in VeraCrypt to drive X letter, restoring the header keys will not fix a corrupted filesystem. However, here are the procedures for future reference.
Using Windows OS in the main window, select your device partition that has been encrypted.
First try to mount using the embedded backup header. When you click the mount button, you will get another pop-up window with a Mount Options button. Click that button and check the box for "Use backup header embedded in volume if available". Then
enter your password and click OK.
If you are still unable to mount the volume and you have the external backup of the header keys as a file, then you can restore the header keys by selecting your device partition, click the Volume Tools button and select Restore Volume Header.
Once you can mount the encrypted volume, you may need to use software recovery tools to fix the filesystem and/or recover files.