You can use the same points, that you used to define the chords, to define the faces. I’m not sure if I should show you how to do that because this is your thesis and I’ll be doing you a disfavor if I give you a solution straightaway. If you face specific difficulties, I’d love to help you with those.
The total number of faces will depend entirely on your UV divisions, so you can get that even without generating any chords or faces.
There might be a mathematical way to calculate the surface of the divided faces as a percentage of the area of a perfect dome, but I’m not aware of such a method. The easiest way to get the total area would be to generate them and then query the area of each surface and sum them up.