How do I copy a sketch and change the orientation of the sketch when I paste the copy in?
You can select the sketch in the tree, then copy.
Select the plane, surface, or face you want to paste it onto. You will need to go into the sketch, re constrain your geometry to relative features or the origin for it to be fully defined again.
Sometimes, I define sketches with construction lines that act as a coordinate system. Then I use NO horizontal or vertical constraints, only parallel or perpendicular to my ad hoc coordinate system.
This way, I can move and rotate an entire sketch by moving the basis construction lines.
2014 SOLIDWORKS Help - Derived Sketches
You could look at a derived sketch to maintain links but move, mirror or reorientate the sketch entities.
Save the sketch entities you want copied as a block, then you can paste, rotate, and scale as much as you want on any sketch planes, and if you want to paste it to other parts you can save the block externally.
Use the Modify Sketch command.
2016 SOLIDWORKS Help - Modify Sketch Dialog Box
Thanks to all who replied. All the solutions suggested work in their own ways.
I failed to RTM so I never knew about/used <DERIVED SKETCHES> & <MODIFY SKETCH>
I have looked at both and it has opened up some new directions to take in the future.
Retrieving data ...