The federal prosecutor investigating the origins of the Russia inquiry is examining testimony by the former C.I.A. director John Brennan and seeking his communications records. The federal prosecutor scrutinizing the Russia investigation has begun examining the role of the former C.I.A. director John O. Brennan in how the intelligence community assessed Russia’s 2016 election interference, according to three people briefed on the inquiry. John H. Durham, the United States attorney leading the investigation, has requested Mr. Brennan’s emails, call logs and other documents from the C.I.A., according to a person briefed on his inquiry. He wants to learn what Mr....