Short answers, pulled from the story.
Jefferson Davis served as the only person to assume the position of president of the Confederate States of America. He was unanimously elected by the provisional congress at Montgomery on the 9th of February 1861.
Jefferson Davis took office officially on the 18th of February 1861 after arriving from Mississippi where he had resigned his seat in the U.S. Senate. A permanent constitution established six-year terms starting the 6th of November 1861 for future presidents.
The City of Richmond purchased the Brockenbrough House for use as an executive mansion known as the White House of the Confederacy or the Grey House. Jefferson Davis lived there until Richmond fell to the Union Army in early April 1865.
The permanent Constitution made the president commander-in-chief of the Army, Navy, and militia under the authority of the Confederate States. The president commissioned all officers of the military and naval forces and could fill vacancies during Senate recesses but could not reappoint previously rejected persons.
Historical records mark the 5th of May 1865, as the final day of the executive branch's existence when the Confederate States cabinet declared the Confederacy dissolved. No successor assumed the office following the collapse of the government.