The only way to sync with a Mac is through third-party apps like
PocketMac (free, but doesn't play well with newer Macs) or Mark/Space's
Missing Sync ($40, no free trial period, no guarantees it will work better than PocketMac).
Like Midnightdraven said, there is no updating the OS without Windows. You can run Windows on a Mac in an emulator like VMware Fusion or through Boot Camp. Parallels doesn't work though. Something about the USB ports not being fully enabled or something.