That is a question regarding the laws of Australia. You should contact an Australian immigration lawyer.

Absolutely, but your departure will withdraw your request for a change of status.

Try inquiring with the social security administration. If that fails, contact your state agency dealing with refugee resettlement for help.

It depends if you were granted a change of status or not.

If you are a U.S. citizen, ad your mother entered the U.S. as a tourist, and you filed an I-130 for her, she can file for adjustment of status now.

Yes, it is considered normal and even customary to do so.

No, it is not likely the consular officer will agree to issue a student visa or tourist visa, when there is an approved immigrant visa with current...

Your spouse's approval is not a prerequisite for the children to immigrate. They can immigrate without him.

You can certainly try. You may be able to convince them that you are the same person as the one listed on the notice.

It may take 1 - 6 months for the interview, and if approved, you should get the card in about three weeks from the date of approval.