The portrayal of FDR is largely accurate to Franklin Delano Roosevelt's reputation at the time. He was a 21 year old Harvard student from a family of privilege in 1903 who was seen as an entitled brat by many including Grover Cleveland. He would marry Eleanor in 1905 and she had little interest in sex (at least with her husband) which left him interested in other sexual pursuits.
The assassination referenced here is to Theodore's predecessor William McKinley (which put him in office). Other historical references include the Cuban-American war and the New Deal.