Can I work or do tourism while transiting on a subclass 771 visa?

The subclass 771 exists solely to let you transit through Australia to a third country. It does not permit work, study, or general tourist activities during your short stay.

If your purpose is anything other than transiting, such as sightseeing, visiting family, or attending business meetings, the Transit visa is the wrong visa and you should apply for an appropriate visitor or work visa.

Using a transit visa for purposes other than transit can breach your visa conditions. Keep your activities limited to what is needed to continue your onward journey.