2. There are a lot of parameters to be considered:
- Radius of the cylinder.
- radius of the base of the cone and
- Height of the cone
- Do the axes of cone and cylinder intersect? If not, how large is the offset?
- How large is the angle included by the axes?
3. I can (vaguely) remember a very hard time before the drawing board when I had to construct the intersection line of 2 cones. You must use auxiliary planes and spheres and the only high-tech equipment we were allowed to use, was a slide-ruler! (This nightmare is now more than 40 years ago, so probably there are a lot of computer programs which will draw the curves)