FAO are available til 8. it took me about 5 mins to get through this time last night

both of you should apply for payment now. there may be a witholding period due to your partner voluntarily leaving work - but it is best to apply now and then serve out the waiting period rather than guessing what it will be - if you wait longer than the designated period, it won't be backpaid

you MIGHT be eligible for parenting payment (as it's there to support your children) but it will depend on whether your partner gets any leave payouts etc.

you would also be able to appeal any decision to not pay based on him quitting if you can provide medical documentation that he was being treated for stress - it's not something i can guarantee would work, but it's always worth trying

don't go into the office - they will send you to a phone and tell you to call as all first contact for payments is done over the phone. call FAO/parenting line 136150 and go through the details now.