What happens? Nothing. You're just going to have to sit the exam without completing the exam.
Can we appeal? Appeal what? To do the HSC on a later date? You can give it a try by writing a heartfelt letter to BOSTES.
Here's some options:
1) What you can do is write an online article and tear down that school's reputation. Get some momentum by making it viral, and then force them to sack the teacher and make a public apology. Hopefully other schools would be in on it, and eventually forcing them to shut down.
2) You could sue them, i don't know on what grounds, but who cares? They are liable for not giving you a proper education. You'll get compensated for it and hopefully you'll be well off.
3) You could just learn the topics by yourself, and completing the HSC knowing that you didn't need a teacher and would be better off at the start of the year if you were homeschooled.