Please remember that im not a master or anything, and take my answers as an experienced students answars.Fighting while doing handstands? Many of the movements in capoeira are ritualised, including standing on the hands in many different ways, witch in african culture often is accosiated with "entering another world" by turning things upside down, besides this there are many powerful and effektive kicks and scissors done by balancing on one or two hands, some of them can be found in slightly different versions in other MA For instance Ahihara karate.
You are very right with the media hype, people like to se things like handstands and jumps very much, this is the showoff part of the art you most likely will see.
Im sorry but i have to go training now...i will continue when i get back.