Does not matter if you are a US Green Card holder or not, when you have an Australian visitor visa, you can go there.
Yes
You can travel within the US with a green card so long as it is valid. A green card is NOT a valid document for international travel outside the US. To travel outside the US, you will need a passport and possibly visas depending upon the passport you hold and the country you visit. Please check with the local embassy/consulate for the most up to date visa requirements for your country's passport prior to travel.
No. NTSA guidelines require a passport (foreign or US), US passport card, green card or US drivers license or non-drivers license.
Yes you can - I travelled to Australia in 2006 w/o my green card - and more importantly, got back nto the US - however you need some official paperwork and a temporary green card + stamp in your passport. Contact US immigration services (uscis.gov is a good start) for the details - it takes some patience to get a real person on the phone - good luck ...
A Canadian citizen with a green card can use their Canadian passport to exit the US and use their US green card to re-enter the US under the same status. Hope this helps.
Yes a AS6 category green card holder can travel to home country. Provided he feels safe to travel to his home country and he is not anymore fearful of the effects of going there.While you travel to your home country you are on your own and since you are not a US citizen the US government will not help if you are in trouble in your home country whatsoever. It may be considered fraud if you got green card through asylum in US and actually you really don't have any issues to fear in your home country.
yes,as long as you have no criminal record.
It depends on where you want to travel to...If you are goin to the UK you can enter with your British Passport. Also you should be fine to travel within the European Union with the same British Passport. Your Green card will give you entrance back into the US when you return.
Having a "green card" from the United States will allow you to enter the US if you leave. It has nothing to do with access to other countries. Whether or not you will need a visa to travel to New Zealand depends on the country from which you have your passport.
Yes provided the trip is unavoidable. Its important for you to have a copy of your old green card and also the notice of application or any kind of proof for having applied for green card renewal.
Using the green card and passport you can travel abroad provided the stay outside US is for a maximum period of 180 days. If you plan to stay for more period of time you should file for reentry permit which is valid for 2 years to reenter US using immigration form I-131 travel document. After a year as a green card holder if for work or any purpose you need to stay outside US you can preserve your residence in US for naturalization purposes later.