What do you mean, I don’t understand
The correct answer is the last one. Kilpatrick's article shares how White House staff feels about Nixon's resignation.
In the article, numerous aides and officials are quoted. Each gives his thoughts and/or opinions on Nixon's resignation. Many are sorry to see him go. Therefore the second option -- that the staff is unaffected -- is not correct.
The article does not say much about who will become president after Nixon. Furthermore, the staff itself is not changing; only Nixon is leaving. Therefore, the final answer is the correct one.
A run-on sentence is a sentence having two independent clauses with improper punctuation and without conjunctions. The correct answer is option b. It is difficult to understand a run-on sentence because you cannot identify where to pause or stop and that the sentence does not have conjunctions which would help in the transition of clauses.