I have the following two circles (n1, n2). I know the coordinates of them. They are connected with a line. I also know the angle "alpha" and the diameter of the circles. Now I try to calculate the coordinates where the red questionmark is. The point where the line crosses the second circle.
How can I do that?

You can draw a horizontal line to the left from the center of n2.
Then treat it like a unit circle and draw a line straight up from the question mark. Then the coordinates would be $$(x_{n2}-cos(\alpha)\times \frac{d}{2},y_{n2}-sin(\alpha)\times \frac{d}{2})$$
Due to alternate interior angles between parallel lines being congruent.