With regards to Medicare eligibility for those on student visas. Touch wood that is all true and correct because I'm lodging an application tomorrow morning - I will post an update after that's done.
For anyone looking at this thread asking the question
"I am currently on a student visa, I have applied for an 801/820 Partner visa, can I get Medicare?"
(I am posting this because there seems to be a lot of confusion around specifically holders of student visas - I was certainly confused about it while going through this)
I can answer a definite "YES, you can get Medicare while on a Student Visa!" now, from personal experience. You do not need to wait for your Student Visa to expire and Bridging Visa to kick in.
You just need to have a letter from immigration acknowledging you have submitted a valid application and the receipt to prove payment. What visa you are currently on seems to be entirely irrelevant (aside
from being a valid temporary visa allowing you to be in the country). My partner and I were sent the letter and receipt by email (.pdf) we just printed those out and took them to our local Medicare office along with the various other documents listed on the application form. The Medicare officer looked them over and looked us up in the online database. She could not find our details listed there, we'd only received the acknowledgement the day before. It didn't even matter that she couldn't find us in the online database because we had the letter and receipt. She added my partner to the Medicare database, printed out a slip with the number on it (we're still waiting to receive the actual card in the mail). We have since used the Medicare number at the local GP and used it to get a Maternity booking at our local public hospital - thank goodness for that too, she's due in January!
I hope this helps someone!