BG got in first. Not much point me trying to explain it!
i did read your post before you edited!

basically a couple of points you raised that should be covered

rent assistance is payable with newstart if you only receive an income support payment - when you have a kidlet, it is payable with FTB as the allowable rent assitance amounts are higher under Family Assistance Law than Social Security Law. it is payable with only ONE payment per couple, so generally it will be paid with your FTB payment unless for some reason you are getting minimal FTBA, in which case it will be paid with the income support of the FTB payee.

when you are partnered, if one is on Newstart, one on Parenting Payment (whether defacto, married whatever) you will be on the same rate of payment.

FWIW - it was mentioned in this post (before it was edited - just as i hit "quote" i'm sure!) that FTB is paid on the opposite week to income support payments. this is a CHOICE - you can have all your payments on the same week, but it means going a fortnight between payments, most income support recipients CHOOSE to receive payments weekly (so ISP one week, FTB the opposite) as it is easier to live knowing you only have to budget for 7 days. fewer people "run out" of money for essentials this way