1) You can apply for Medicare now. You do not have to wait for the BVA.Thanks guys. So to sum up:
1- I can apply for Medicare now
2- I can go out of the country without informing the immigration ( as long as the visitor visa is still valid).
3- I have to wait until 3months stay of visitor visa is over, so the BVA will be in effect immediately.
One more question: Is it a must to submit the Form 80 and National Police Check of my husband ( sponsor) now or we can wait until the immigration requests us to provide? My husband is Australian. Some of the questions in Form80 seems not to apply for him. I wonder if it only applies for people with PR?
2) You DO have to inform immigration if you leave the country even if you're still on your visitor visa, as they cannot grant the 820 visa if you are offshore.
3) Yes. If you leave and come back, your BVA will not kick in until you pass the new 3 month window that will be reset when you re-enter the country. As others have told you, if you cancel the visitor visa, it will cancel your BVA and you'll be here illegally. Do NOT cancel your visitor visa!
Do you have children? If so, your husband will have to do an AFP check. If you don't, they may not ask for it. If they do ask for it, it only takes about a week to get in the post.