4) This situation (and similar ones) happen all the time on movies, TV shows, etc. Honestly at this point this is a go-to plot hole that everyone turns a blind eye to.
Consider how many times it would have happened on Captain Awesome... Lux probably wouldn't forget
She did suggest that the gun would be hidden in a spot where only a proctologist would find it.
Lux shook her head "I don't know what was up with that drone... I guess someone might have accidentally activated it?"
She then carefully stepped out from cover with her hands in the air "Not saying it was me though. I certainly didn't see an auto-doc and went to run a diagnostic on it..."
You turn your back for one second and a machine on standby vanishes, she thought to herself with a smile.
"Anyway, you're safe... relatively speaking" Lux continued, walking over "You took a nasty hit in the last battle and we had to tow you here. Eden says it used to belong to a smuggler or a broker or something. Point is, everyone's here and worried about what happened to. Yes even Eden. Although probably more about your ship than you"