__As to your first question. In many cases, you might not project a curve, but instead, in one of the orthographic views, cut the surface directly. This saves a step, so why bother to project the curve and move the endpoints? Well, I started out doing it that way, and I found that too often I ended up with spurious endpoints; that is two or more "endpoints" very close together. Which one is the "right" one? In some cases, I ended up with three or four "endpoints". This led to all sorts of problems, so I had to find a way to work so that I only had one true endpoint or intersection. I can't tell you why we get these errors. In theory, the points should work out right, but in practice these errors keep coming. I call them "rounding-off errors". In any case, when I project lines and adjust the endpoints, I eliminate the errors.
__As to your fillet problem, this was simple. First, I copied the cylinder where you had projected the curve and cut the hole. Then I copied the other part and aligned them. I then made the blue curves and did a 'Blend' between them. This is using 'Blend' with curves only, not surfaces. I then projected the red curves onto both objects and did another 'Blend' between them. Now I could use 'Network' with three true cross-sections between the two objects. It's the same, top and bottom. You can see the result with the edges hidden. It's not quite perfect. One more step would project two more lines and due two more blends to get two more cross-sections, between the ones that I did the first time. You have to give 'Network' enough information to work with. In this case, only one cross-section between the ends of the fillet is not quite good enough. Obviously, if I wanted to I could add as many more cross-sections as I thought necessary, but you can see that only one (between the ends) looks good and you have to look closely to see that between those sections 'Network' has exercised a bit too much "imagination".