There were no changes regarding keyboard shortcuts in 2016, and all of the commands you mention are available for keyboard shortcut assignments.
The only thing I can think of is to make sure you are in the Part environment, and not Assembly or Drawing.
Hope this helps.
Thank you for replying so quickly. I have just closed and re-opened SolidWorks, created a new part and voilà, the shortcuts were available to assign. the only thing I can think of is the part I had open previously had been created in SW2015 and imported into SW2016.