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There is an awesome calculator tool on the centrelink website. You can put in all your financial details and see what you are eligible for per fortnight.
Uh no they are not likely to back pay you. You get paid from the date of the claim, not date of birth. Also, what on earth have you been doing!?
I think you can contact Centrelink, and lodge an 'Intention to Claim', they usually back pay from then, but I'm not sure of all the payments types that this applies to. Call Centrelink, or enquire online asap.
You need to do paperwork asap, it takes a while to process, up to 6 weeks they say but can take longer. You would need to call them regarding payment and whether they back pay you from start of claim or from birth, I don't know what that works