Your tracking is obviously not working very well. You need to carefully make sure that the track points stay stuck to the reference areas. The most common problem using AE's tracker is that people grab too few pixels. They try and track something that is too small. You want to use scale and rotation and select a pair of good reference points. The eyes would be my first choice. Then carefully track the face you want to replace, apply the transformations to a null, then position your replacement face and make it the child of the null using parenting.
If you want different side views then you'll need different images and you'll need to morph them from one to another.
If need to change the picture for different angle, does it mean that I need to set the main picture invisible once the first angle is no more?
I have been thinking how the Framy app does the face changing in different side views. I wonder how do they do it?
It looks like Framy is mapping a still to a 3D model. You are trying to map a still to a 2D video. Different process. From what I can see in Framy demos they have a bunch of animated 3D poses and then you just add a still. It is masked as an oval and applied as a texture to the 3D model. Simple as can be.
You can use projection to map your still to a 3D shape in a 3D app or in C4D, or you could simply make your still a 3D layer and animate the y rotation. You could use corner pin tracking or Mocha to replace track the angle changes in the face and simulate the rotation of the face by distortion.
Rick, thanks a lot for you too look at my AE and your advises about Framy app.