When I applied for my 1st stage defacto visa, I was told by my Case Officer that my visa process would have been quicker if I’d submitted a Aus police check with my application. I'd been here only 10 months when I applied, so didn't think I’d need an Aus one as it advises on the form to get one if you've been here for over 12 months. I'd only supplied a UK one. Whilst they accepted my application, I was told it'd be pending until I obtained a Aus police check which wasn't bad, only took a couple of weeks.
Medical, our Case Worker told us who to go to. It was a designated Medical Centre in Sydney CBD. We just called up and booked an appointment. Not sure where you are, but the immigration office should be able to tell you where to go.
Proof of our address, we met in London and only had proof we were living together since being in Australia 10 months. We did however, have lots of proof we had been in a relationship for 18 months at that point. Lots of flights here there and everywhere before arriving into Australia. Plus, we'd spend 2 months in Asia before arriving in Australia, so they counted that as a part of the 12 months proof. Try not to over think whether your application looks like you're lying, I was crapping myself when I was filling out the forms, re-checking over and over before I handed them in, so I can definitely appreciate what you're going through. I also had both sets of Parents write a letter verifying our relationship, which our Case Officer said was a good idea when he looked through our application.
I was lucky, I met my case worker. Most people I know that have gone through the Defacto visa process don't meet him/her.
Have everything ready, definitely the police checks.