if you want to apply for EAS, the forms get sent out to the schools, so you need to speak to your year coordinator or careers advisor. This is for things like prolonged injury or illness, financial hardship, personal issues eg parents getting divorces, close relative dying etc that affected your study throughout year 12. You will have to show proof, like, doctors certificated, evidence of centrelink payments, death certificate of relative etc.
If something stuffs up your study right before the HSC, like you break your arm, or you are sick and miss an exam, thats different, and i'm not sure about the procedure for that.
Usyd usually requires you to have significant evidence of hardship, they accept people willy nilly. But it is very subjective, so it differs for each person who applies.
The EAS scheme can let you in for up to 5 UAI points lower, but it varies according to the course, and every year it changes. Eg. I applied with EAS for Vet with a UAI of 97 (cut off was 98) and missed out, but the next year, someone got in on EAS with a UAI of 95. Your level of hardship doesnt affect how many points lower you can get in for. Usyd sees it as you are either disadvantaged or not, and of the disadvantaged ppl, the top few for each course will be accepted. so obviously in my year there were disadvantaged people applying for vet who got UAI's higher than mine (but still lower than the cutoff).
hope that makes sense.