a$.$ The five inversions of the array $[2,3,8,6,1]$ are: $(2,1),(3,1),(8,1),(8,6),(6,1).$

b$.$ The array with elements from the set $\{1,2,...,$ n$\}$ that has the most inversions is the array sorted in descending order. It has n$($n$-1)/2$ inversions.

c$.$ The running time of insertion sort is proportional to the number of inversions in the input array. This is because each inversion corresponds to a pair of elements that are out of order and need to be swapped, and each swap takes constant time.