Still, Mr. Pruitt and his team obtained many of the perks he wanted. Staff members questioned, but nonetheless approved, frequent trips that routed Mr. Pruitt through hub airports that allowed him to spend weekends at his home in Oklahoma. The administrator also had charter flights approved after they were already taken, the public records show.

“This memorandum responds to your request for written approval for the Administrator and three EPA employees to use a charter service to fly from Denver to Durango, CO on August 4, 2017,” read a memo written in late August, after the trip was completed. The approval covered a charter flight to tour the Gold King Mine near Silverton, Colo., after Mr. Pruitt’s commercial flight to Denver was delayed. This 40-minute flight cost $5,719, the records show.

Other memos released through the open-records law show that Mr. Allen handled requests for renovations to Mr. Pruitt’s office. “I spoke to Gayle and we can proceed as it is not part of the $5,000,” read an email to Mr. Allen in April 2017, as staff members were being pressed to find a way to spend more on office renovations than was allowed under federal guidelines. In this case, the expenditure involved a biometric lock and was not counted against Mr. Pruitt’s furniture budget. “Approved,” Mr. Allen wrote back.

The documents do not reflect the behind-the-scenes friction between Mr. Pruitt and the senior officials, but several agency staff members said in interviews that they avoided putting objections into writing because they suspected there would ultimately be an investigation into the matters.

Mr. Weese, the security official, questioned Mr. Pruitt’s desire to use flashing lights and sirens in his motorcade — a perk more commonly associated with the presidency — according to three of the people who worked with or for the E.P.A.

Mr. Pruitt, who often ran late, wanted to use the lights and sirens to expedite local trips in Washington to the airport or to dinner, including at least one trip to Le Diplomate, a trendy French restaurant that he frequented. Such use was not consistent with agency policy, but Mr. Weese was unsuccessful in stopping it.

The agency said Mr. Pruitt played no role in deciding when the sirens and lights would be used. “The security detail for the past 15 years has used them in very limited fashion,” Mr. Wilcox said.