Hey, I have spent two summers working at a girl scout camp in California each camp is different but at my camp this is how it went:
1) As a general counsellor we did spend time with solely are units leading activities, there was always at least one other counsellor with you. However, this was for a maximum of a couple of hours a day.
2) My camp was single sex, but i highly doubt that aca (the accreditation systems camps go through) would ever permit mixed cabins.
3) My camp didn't have a brother camp, however just because a camp is single sex for campers doesn't mean it will be single sex for staff. My camp certainly employed staff of both sexes.
4) Medical examination just has to be done in time for camp; you just have to have it with you when you turn up at the airport.
5) There are normally a couple of orientation day’s u.k. Around march/April time i believe (not really sure). However, i didn't go to one either of my years at camp so i can't tell you anything about them!
6) I certainly experienced difficulties with kids while I was there however, anything major you can just call in your ad staff (camp directors etc) for back up. I highly doubt that at any camp they would leave you with things you can't handle!
Enjoy your summer, am sure you will have a fab time!