If X-ray had existed James A. Garfield may have lived?

Answer 1

Probably not. What killed Garfield was the ineptitude of his doctors who refused to believe that germs existed and rejected Joseph Lister's advocacy of sterilization. This is especially the case since the Doctor Who appointed himself the head of Garfield's medical team, D.W. Bliss, explicited rejected Dr. Lister's methodology as a bunch of hokum.

The first doctors who treated Garfield on site at the Baltimore-Potomac train station laid him down on the dirty station floor and poked around in his wound with unwashed hands, likely causing from the get-go the infection that ultimately killed him. Not only did they not make sure their hands were clean, they subsquently repeatedly used unsterilized instruments to poke inside his wound.

Moreover, the bullet in Garfield's body was not in a fatal position, lodged as it was in some fatty tissue behind his pancreas. He would likely have been able to survive with the bullet in his body.

Having an x-ray and knowing where the bullet was lodged in his body might have prevented the doctors from probing his open wounds more than they did, but it would probably not have prevented his death via infection.

Answer 2

Perhaps, but he died of a serious infection and there were no antibiotics at that time.

Answer 3

Yes