When Bobbie is sitting in the Razorback after the battle, she plucks a bullet out of her suit and throws it behind her. It tinkles on the floor, which it shouldn't do since they're in zero gravity.
Secondly, why would you leave a heavy object lying around in a racing ship prone to sudden bursts of acceleration? That bullet could harm one of the passengers or create damage.
Cyn would not have died the moment the air-lock door opened as shown. There would have been plenty of time for Filip to get him back inside. This was even shown by the fact Naomi was still alive and conscious enough to use the injector thirty seconds later.