Oh WOW hun, is this sudden? C'link is absolutely flooded right now, the holidays see many, many people splitting up .

Head to the Clink website, there is a calculator there and you can enter your circumstances and see what you are eligible for. If you are eligible -

You can get paid from the day he moves out.
You will receive max rate FTB A and B.
If you are receiving mat pay, you will be paid based on how much that is each f/night.
Parenting Payment is based on the fact you are a parent caring for a child, not looking for work. It won't matter if you don't go back to work, or don't look for work until bubs is 6 or something so a long way off. If you resign, it doesn't matter.
You won't get Rent Assistance, cos you are not renting.
Your FTB may be affected ONLY if he has to pay you a huge amount of CS.

hth xoxoxoxoxo
Sorry about the split mate XOXOXOXXO