Hi,
My name is Federica and i'm italian,
sorry for the orrible english...
I would ask you...How to attach a satin ribbon on a Fondant Wedding Cake like in this photo?

I wash my ribbon and lay it out to dry overnight. Ribbon spots really easy, so I lightly rub crisco over mine completely. This eliminates the grease spotting. Pull the ribbon around the cake and dot it on the back side with a dab of icing. The crisco and the dab of icing helps hold the ribbon in place.

I put clear tape on the back of my ribbon, just one strip through the middle and then attach with dots of icing

I have never used anything other than Crisco. I am not sure what your vegetable fat is, but try on a small piece of your ribbon. The crisco will make the ribbon a little deeper in color. I would think as long as it didn't change the color you would be okay. I actually practiced on a small piece of my ribbon, before I started putting the ribbon on cakes.

If the ribbon is going on a fondant covered cake there is no reason to grease the back side with Crisco or any other shortening. There is no spotting on the ribbon on fondant only when it is directly on buttercream. If the cake is round like the one in the picture you can just simply wrap the ribbon tightly around the cake and attach with dot of royal icing at the point where two ends meet, then cover with the bow. I have also very lightly misted a little water on the ribbon and it will stick to the fondant.