Isn't the angle a result of a calculation when the position of a point is changed?

No, it is a given value and represent the plane slope. The skeleton algorithm calculate the planes intersections.
When I change the position of a point, a new plane will be calculated that passes through that new edge, BUT at the same given angle.
The result of intersections of planes will not always be as you want, so you will have to manually change the slope on almost all faces.
This is how I finally got some sort of triangles.

use triangle faces and don't try to force rectangular faces

I know this and used triangulation to calculate the area of each visible face to get a total roof area.

texture direction towards the lowest point.

Finally that's OK even for me [B-)]

PS. The Terrain generator modify the vertices and the resulted object cud be used as something else (eg. an irregular roof).