Last January, six months after Fox News ousted its chairman amid a sexual harassment scandal, the network’s top-rated host at the time, Bill O’Reilly, struck a $32 million agreement with a longtime network analyst to settle new sexual harassment allegations, according to two people briefed on the matter — an extraordinarily large amount for such cases. Although the deal has not been previously made public, the network’s parent company, 21st Century Fox, acknowledges that it was aware of the woman’s complaints about Mr. O’Reilly. They included allegations of repeated harassment, a nonconsensual sexual relationship and the sending of gay pornography...