Can I copy one sketch to another plane which is not parallel to the sketch plane?
Yes you can. Choose the sketch to copy > Edit from top of screen, select Copy, select new plane, > Edit and paste to the new plane.
tutorial - how to copy sketch to another plane
Exit from sketch and choose sketch from feature tree. then go to Edit>>copy. Be sure that sketch must be closed and selected. if you don't, copy button will be inactive.
Open sketch on o plane and Edit>>paste
Now you can position. You need to drag and drop holding the lines because if you drag the point, only that point will move.