Not sure what the visa situation is for you but from my experience applying for and getting an Australian visa is a very straight-forward process. It's all done online and you usually have a confirmation within the day. Might as well do it to have the option if you need it.

As for what to do for 3 hrs, I'd stay in the airport if i were you.

Ok, if EVERYthing went very smoothly for you, it might be feasible to take the train to Circular quay (about 30 minutes IIRC and they run every 10-15 minutes), have a quick look (more like a quick glance) at the Sydney harbour bridge and the opera house and go straight back. But you'd be rushed. A lot.