Please see my answers below:
1. Is there any minimum duration to stay in Australia for Port of Entry ??
No ,In fact you can just get your passport stamped at the immigration and catch the return flight with out even stepping out of the airport.
2. When we reach Australian Airport, what do we have to do actually. I mean do we have to visit any office. Is there anything done to our passport when we cum for port of entry? How will be know that our PR is validated?
Every thing is linked with your passport,when they swipe your passport or I will say before you travel itself they know your passport number and they are well informed that you have a valid visa,I think they dont even allow you to board the flight if you dont have Visa.
3. Can you suggest any city to travel to for Port of entry. I am planning to cum and move by next flight after a gap of some 8-10 hrs, after doing some shopping at Airport
I had not been there to Aus,so do not kow much about the cities.And Why do you waste such money only for shopping and flying?
Just spend a couple of days,I would suggest a week and do some sight seeing,book a hotel/youth hostels or some cheap accommodation for a week.search airbnb.com etc.. you will get it around 50$ per day.
4. Do i need following while doing just port of entry ::
4.1 TFN
4.2 Opening of Bank Account
4.3 Registration in Medicare
4.4 Registration In centrelink
No ,you can do it in your own sweet time after you get out of the airport and settle down.
5. If my husband cant travel with me without a valid parnter VISA, Will my parents be able to travel with me without any VISA??
No,Every body needs a visa,even babies who are days old,unless they are born in Australia.
6. Do i have to do anything in VEVO, registration etc or its a portal just to check VISA status.
NO Idea on this,may be some Mod/senior can answer this.
7. Whats the cost and duration of processing of a permanent Partner VISA.
Partner visa is taking around 1 to 1.5 years(YES YEARS not Months).Once You apply for this partner visa he can stay with you in Australia till he gets his Visa granted.May be confusing to you please check immi.gov.au on partner visa it is clearly explained.
Hope this helps.
All the best with your move.