for 3, removing the "reverse duplicates" of permutations is as easy as taking 
the top half

  (i.@! A. i.) 3 
0 1 2 
0 2 1 
1 0 2 
1 2 0 
2 0 1 
2 1 0 


last (5) is reverse of 0.  4 is reverse of 2, and 3 reverse of 1

Is there a function for producing permutations without their reverse included?
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