Short answers, pulled from the story.
Harry Hopkins is credited with suggesting the phrase directly to President Franklin D. Roosevelt. Another account claims William S. Knudsen, a Detroit auto executive, provided the idea when Roosevelt tapped him to lead war material production efforts.
Franklin D. Roosevelt delivered his radio broadcast on the 29th of December 1940. This speech occurred nearly a year before the Japanese attack on Pearl Harbor which led to United States entry into World War II.
General Motors converted civilian manufacturing lines into massive production facilities for trucks, tanks, and aircraft parts while Ford Motor Company produced trucks and aircraft. Chrysler built tanks, electronics, and trucks alongside their automotive work and American Locomotive Company built tanks for armored divisions.
Defense spending distribution allocated 32% to aircraft production during the war years. Ships received 14.8% of total military expenditure while ordnance including guns, ammunition, and military vehicles accounted for 25.6% of costs.
The phrase Arsenal of Democracy appears carved into stone at the Franklin Delano Roosevelt Memorial. An exhibit titled Arsenal of Democracy exists at the Michigan History Museum to honor the era.