Mostly worn by Gentlemen, not for the hoi polloi. It’s a duelling sword / fashion accessory / symbol of rank depending on the time and the individual. Primarily worn at court and in town rather than on campaign though officers may have carried them on campaign, again as a symbol of rank.
Depends. (Haha)
Was the non speakers mic turned on while the other candidate was speaking? Makes more sense for it to have been trump in that case. Also depending on the mic type I’m not sure how well they pick up ‘distant’ noises like that? I would guess there are also some room mics to pick up audience reaction and questions, could have been off one of those. But I don’t know much about microphones so I don’t know about that.