score:1
Typically, to apply for a visa for country C from within country B while being a national of country A, all one has to show to Cβs embassy in B is proof of lawfully being in B.
Thus, as you are legally (temporarily) residing in Australia on an Australian student visa, you can apply for whichever visas you need from within Australia at the embassies these countries have in Australia.
Cases in point: as a German citizen residing in Japan, I successfully applied for a Chinese visa from within Japan. Likewise, when I was temporarily residing in Finland (though not registered as a temporary resident because I was below the 90 days limit), I applied for my visa to Russia in Finland.
Upvote:4
You are a resident of Australia and you are entitled to apply for Singapore Visa from Australia itself.
Also, since you have Visa for Australia / USA, you don't need Visa for 96 hours of stay if you are transiting to another country.
https://www.ica.gov.sg/enteranddeparting/before/enteranddeparting_before_vftf