But were they [angels of the faces] changed when the angel of the faces were turned for the fusion of the photographs?
The FS image was rotated. Take a photograph, lay it on a table and spin it around. That's rotation. However, on a computer there is a chance of distortion when images are rotated, so steps have to be taken to minimize the distortion.
Sorry to harp on this, but this is not fusion. Fusion is similar to morphing. If you took a photo of AA and FS and morphed a composite image, that would be fusion.
Fusion would be inherently deceptive in this case.
All that was shown in the NOVA documentary was a dissolve, a basic transition used in movies and television. As far as I can tell, the computer only replaced the photos and transparencies that an expert would use manually. And it added a dissolve. Here is a simple dissolve, part of a PhotoShop tutorial:

Also, what are the numbers on how many peoplefaces when using points are similar and if it's even a good method of using accept in the process of elimination.
I know facial recognition is now being used at airports and sporting events to spot terrorists, and in prisons, banks, and other secure facilities. One proposed future use for face recognition, as costs go down, is a replacement for PIN numbers at ATMs.
We'll know a bit more about these systems in the fall, when the US government publishes its findings on its latest face recognition vendor comparison. The comparison will take place in August or September.
I suspect that a face recognition system will find that AA looks like FS. And that she looks like AN. This case has so many bizarre coincidences it wouldn't surprise me.
A face recognition system uses nodes, or vector-based points. The nodal points are typically expressed as XYZ coordinates, with X being a horizontal distance, Y a vertical distance, and Z a nearer or further distance. These points are not dots or pixels; vector-based graphics are mathematical and usually have an accuracy of at least fourteen significant digits of precision. That's why, for example, a circle drawn in a raster-based paint program will look jagged when zoomed in, but will look round in a CAD program regardless of the zoom factor.
This image, from MIT's site, shows nodal points used for face recognition. Typically, face recognition systems use a dozen or more nodes, but only four are shown here: the pupils of the eyes, the tip of the nose, and the midpoint of the mouth.

As for the images of Alexei and Filatov, there are lots of inaccuracies. Look at the line ruled through Alexei's eyes - tangent to the outer part of the bottom right lid and the inner part of the left. There's a similar problem with the line ruled on the photo of Filatov. Look at the lines for the included angle of the faces; the lines on the right side of the faces are tangent to the cheekbone and jaw, but the other lines are tangent only to the sideburns and have no other point of tangency. Also the line ruled through Alexei's mouth is off; it should be slightly lower. IMHO the images are so full of drafting errors that they're pretty much useless.