Do the VC-25 aircraft used for Air Force One carry missiles to protect itself and its passengers?
If so, can these missiles be fired at potential threats?
Near as is know outside of a security clearance the answer is no, a Boeing VC-25 does not carry missiles or offensive weaponry. During times of crisis, VC-25s are often escorted by armed jet fighters which can attack potential threats to the VC-25 if need be.
Following this source, the armament is "none".
An aircraft so big looks more like like a bomber, and large bombers in these days tend to rely on the escorting fighter aircraft to defend them. On board self-defence weapons of the bomber are not efficient, see this answer. I think VC-25 just does the same.