good points.
I know pigeons were used in WWI to communicate between the front and HQ where there were no telephone lines. By WWII, semi-portable (about the size of a briefcase) radios were already in common use. The logistics of delivering and keeping pigeons seems awfully awkward for a secret agent working behind the lines. Keeping, hiding or disguising pigeons sounds even harder than concealing a radio.
As for how the pigeons are trained, I don't know.