Hi Kaus,
Welcome to the forum.
Not sure how long the paperwork takes but you can check out
timeline and that may give you some idea.
Take a look at the the "Helpful website..." post at the top of the forum.
That has links to the visas and should be able to answer that question. I would have thought yes you'd need a medical since it's the fact that you are coming into the country not whether you are permanent or not.
If you google medical insurance you should come up with a link to iselect.com.au. It's one that's advertised a lot here for medical insurance but I've not used it. It gives free quotes and that should give you an idea about insurance costs.
Hope that helps,
Karen