The bomber's engines burn after the plane is hit. Neither the pilot or copilot make an effort to use the fire extinguishing system built into the engine, which would have been the first step of any qualified pilot. Had this been done, given the rugged nature of the B-29, it is quite possible the aircraft could have carried on to its destination.
Aircrew did use throat mics, as you see in the film, they would constantly be taking their hands off the controls. They had a radio button on the joystick to transmit, which activated the mic, they did not have to touch it.
Except for the two B-29s which actually dropped atomic bombs, no aircraft in World War II every carried a fully assembled atomic bomb, or even all of the unassembled components for such a bomb. Due to their weight and size, the casings and heavy components of bombs were sent by ship. Many of the internal components were flow to their destination. A B-29 required special modifications to be able to carry an assembled atomic bomb.
The M1 carbines used by the Americans are shown as having to have the bolt manually operated after each shot, whereupon the casing ejects. In fact, the M1 gas operated carbine had a 20 (or 30) round magazine, and was a semi-automatic rifle, self-ejecting and loading the next round. It could handle rapid repeat fire by simply pulling the trigger quickly. (The M1 carbine is a different weapon to the M1 rifle (aka Garand) which is not seen in this movie)