First victim's surname is shown written on a post-it as "Fergusson", but elsewhere the name is spelled as "Ferguson".
Senator Mayhew would have no authority to dictate hiring responsibilities to Agent Prentiss. The FBI falls under the Executive branch, not the Legislative.
OPR stands for Office of Professional Responsibility, though there is no OPR unit in the FBI. The OPR is part of the Department of Justice and is responsible for investigating attorneys that work for the DOJ who are accused of criminal misconduct, such as United States Attorneys (the federal version of a District Attorney). Allegations of criminal misconduct against DOJ employees who are not attorneys, such as agents of federal criminal investigative agencies, are investigated by agents from the Office of the Inspector General.
Ned offers to give the agents of the skeleton BAU his passwords so the agents could do their own "deep dives" on victims. This action is a violation of a policy known as separation of duties, which ensures no one person has too much access to a computer system, usually to protect organizations from embezzlement or industrial espionage. In an organization like the FBI, separation of duties would be even more important to protect sensitive information.