Hi Donatien,
From your description I'm going to point to the document scanner as the problem. When you make a photocopy, you're actually dealing with two separate systems; the scanner and the printer. Given that you can send documents to the printer from the computer and they work fine, that says the printing system is okay.
So the scanner consists of about three different mechanisms; there's the motor that moves the scanning mechanism when not using the ADF; you've eliminated that as a source of problem because it does the same thing on both flatbed and ADF scanning.
There's the light source that illuminates the document being scanned; that's easy enough to diagnose because if you open the cover and hit copy, you'll be able to see the bright light illuminated across the width of the page. Since you're losing almost a third of the page when scanning, it should be pretty obvious if the light source isn't working right.
The final part of the scanner is the CCD array that reads in the line of pixels. With your set of symptoms it seems pretty definite that's where the problem is on your machine. It could be something as simple as a loose connection on the flex cable that connects the scanner head to the motherboard or it could be a failed CCD array, meaning you'd have to replace the scanning head.
I'll have to leave anything more specific up to someone who has more experience with this particular machine than I do; the information I've presented is of a generic nature common to most multifunction printers.
Hope this helps.