Last known picture of Abraham Lincoln

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Ostendorf recorded that photographer Henry F. Warren from Waltham, Mass. "made three pictures of Mr. Lincoln, one standing, and two sitting." and he stated that it was on the south balcony of the White House, late afternoon. The two seated poses (designated O-112 and O-113) were made on a chair which Lincoln himself carried out on the balcony. The standing pose has never come to light (is lost). I’ve still some questions.

(1) Where was that “south balcony”? Was there in 1865 a balcony at the south front of the White House?
(2) The photographs were made during an impromptu session. I suspect that Mr. Warren was not invited and had no access to Lincoln on March 6. He had made photos of Tad on March 4 or March 5. I think on March 6 he came to the White House to show the result to Tad, made the (impromptu) March 6 photo of Tad in front of the north facade and used the boy as an intermediary to gain access to the President. Comments?
(3) Was O-112 or O-113 the “last photo” of Lincoln? Of course this is a hypothetical question, but is it somewhere documented that O-113 was made after O-112? O-112 is the one distributed by Warren and maybe therefore seen as the “last” photo. Personally I find O-113 a more expressive one, maybe because Lincoln’s chin is slightly higher and his hairline a little different.

The March 4/5 photos of Tad
   

O-112 (left) and O-113