First, let's establish whether the kabane died. I think all kabane killed through penetrating the heart has the blue spark animation. All other kabane are either not killed or killed through means like cutting off the head.
Mumei has only fought with pistol for a few episodes so far.
Episode 2: There is only one kabane killed by one shot and by the speed of the motion, an earlier shot is implied. All other kabane are either killed by two or more shots or impaled by other objects while being shot. It seems to imply that first shot break the metal cage and second shot destroy the heart. The pistol is either slightly more powerful than rifles or are at the same level. However, no human are able to shoot twice at the same spot, thus no kills were made. That might also be the reason there are two pistols in the setup. This may be achieved through improved senses by the kabane virus.
Episode 4: Kabane's bones seem to be reinforced by the virus as well as the katana seems to just bounces off a kabane's skill. This might mean that inaccurate bullets will have no effect at all as they will hit bone. As Mumei is jumping over the top of the train, she seems to one shot three kabanes. We should note however, blue sparks did not appear, which means they are not dead but probably only thrown off the train. However, later on, Mumei clearly killed a kabane through one single shot to the heart. I assumed that is because Ikoma upgraded Mumei's weapon, however, it is yet to be confirmed.
Episode 5: The "Young Master"'s faction is clearly aware of gunpowder weapons as the Ear pulled out a pistol similar to real world weapon rather than steam powered. And he is clearly aware that it can kill Kabaneri. It could be that Mumei's faction and thus their weapons are also using gunpowder before meeting Ikoma. In this episode, Mumei is clearly able to kill kabane in one shot, first weakened by the explosion of suicide bombs, later in completely normal scenario below the crane.
In conclusion, I think Mumei's gun is either as powerful or slightly more powerful than the steam rifle. Thus needing two shots to kill kabane at the beginning. However, starting from episode 4, Mumei's gun seems to reliably kill kabane in one shot. I believe while being trained by Mumei, Ikoma improved her gun. It is just like how Ikoma improved the samurai's sword and the rest of the steam guns during episode 5.