GMAT Critical Reasoning (CR) | If Shero wins the election, McGuinness will be appointed hea

Hi Experts,
I am having a tough time implementing necessary vs sufficient conditions to actual OG Qs:
My basics:
sufficient will lead to necessary but necessary may not always result in sufficient condition to occur.
negating necessary will result in sufficient condition not have occurred
Also usual structure is as below:
If (sufficient condition), then (necessary condition)
Unless (necessary condition) sufficient condition follows.

Based on this let me present argument understanding and my