In NSW do not expect a student discount as it is only for NSw resident students with a NSW current student card (e.g University of Sydney).

You might ask Rudi and other regulars about their Senior travel experiences in Australia - in the Seniors Travel forum, as it is largely focused on this topic. Consolidated Senior discount thread for local travel.

In NSW I believe a Pensioner Concession Card or Seniors Card, for local residents only, is required for pensioner prices. For NSW 131500.info is a good place to start as you will find info on trains and buses.

That's the easy part.

For long distance travel I would highly recommend budget airline flights which are often on sale.
Go to the Other Australian/Asian forum to find some deals. JetStar, Virgin Blue and Tiger might offer sale fares for around $50-60 each way, which will likely cost less than train or bus tickets.
Just google each airline and sale. JetStar and Virgin Blue usually match each other's sales, so check both.