Sydney has a curfew, pretty sure its 11pm-6am-no passengers landor take off between that-so the latest sign off would be like 11ish. You may have to look into the whole transport thing a lot more. They only need to give you 2 hrs notice when your on home reserve, keep that in mind when looking at public transport.
Just go to your doctor and tell them that your jaw is cracking sometimes and that you have a 'friend inmed school' who recommends that you get a OPG to make sure its nothing to worry about and that you would like one as your really concerned about. Or pay the $95
. If you do pay for it, keep the reciept-tax deductible I think as its for work, same as the medical and security clearance