How do the military pilots of Air Force One train for exceptional circumstances in an airliner not designed for high performance?
Does the United States Air Force retain identical aircraft not
  routinely used as Air Force One, for specific training use?


The Airforce maintains two identical versions of the VC-25A that it uses to fulfill the role of Air Force One but its unclear (and likely not public) if any practice occurs in either airframe. 


  Otherwise, how is it determined that these manoeuvres are feasible in
  such an aircraft and that the pilot is capable of performing them?


Through testing, as is the case for the operational envelope of any aircraft. Due to the nature of Air Force One this data is not (as far as I know) public. 

On any note the pilots, who are typically career Air Force pilots all have lots of experience and in some cases experience flying other heavy or high performance aircraft as is the case with one of the most recent pilots


  Col. Tillman's distinguished career spans 30 years in the United
  States Air Force. Utilizing his Bachelors of Science degree in
  Chemical Engineering (Tulane Univ '79), he served as a Rocket
  Propulsion Engineer upon entering the service but was quickly selected
  to attend USAF pilot training. His flying experiences include time as
  a T-37 Instructor Pilot for undergraduate pilot training, C-130
  transport pilot, VIP airlift as a pilot in the Gulfstream III and IV


The air force trains for low altitude and evasive maneuvers in the C-130's not infrequently. I fly fairly close to a major air force base all the time, if you pick up flight following and get handed off to their tower you will often get a warning of such activity. You can generally see it out the window as well (its pretty neat). Presumably an force pilot coming from a C-130 background has some experience flying evasive maneuvers in heavy aircraft.