Complexities of basic operations of searching and sorting algorithms
For general algorithm of bubble sort worst case comparisons are $\Theta(n^2)$ But for special case algorithm where in you add a flag to indicate that there has been a swap in previous pass. If there were no swaps then we come out of the loop since array is already sorted. In this case comparisons are $n$ not 0.

For Quick sort you have mentioned that worst case swaps are $n^2$. Well worst case scenario for quick sort is when all elements are in sorted order thus there won't be any swaps so it should be zero.