1. This depends on your canton so check with your migration office to see if it's allowed. I did read that B permit holders weren't allowed to in one of the other cantons. An au pair probably wouldn't fit the bill anyway as you're supposed to be at home 50% of the time when they're working.
3. If an EU nanny is prepared to move from Germany to Switzerland and apply for a permit then yes I think you can hire her. Not sure if a G (cross border) permit would be applicable if they wanted to continue living in Germany and work in Switzerland, but that may be another possibility. You can't hire a non-EU national as it's not allowed unless they already live/work here and have a valid permit.
Some info on conditions/regs for hiring of domestic helpers and au pairs. http://www.perfectway.ch/en/for-fami...formation.html
and NAV for canton Zurich: http://www.perfectway.ch/fileadmin/d...AV/Zuerich.pdf