US residence status only removes the need for a visa for the USA. Outside the USA it has no validity, it is your Turkish citizenship which determines whether you need a visa or not.
See the link below for a full list of visa-free countries for Turkish citizens.
no
No.
Yes, as a US permanent resident, you can travel to Canada.
Yes, permanent residents of Canada can travel to Canada with a valid Permanent Resident Card or Permanent Resident Travel Document.
Nowhere except when on transit in europe.
A Turkish people may visit Turkey with his nation Id proof. But when he wants to visit his country I don't think there will be such place he could travel without having a VISA. However, turkey is really a nice place for have the tour. I had a tour from there three months ago and thanks to "Citadeltours" for providing us best travel service from my home city Canada to Egypt.
Yes, a US permanent resident can travel to Japan. They will need to obtain a visa before traveling to Japan.
Yes if you have a Permanent Resident card; however, if you do not have a Permanent Resident card you would need to apply for a visa in advance.
No. A passport is absolutely required.
No
Yes, an American permanent resident can travel to Canada with a valid passport and may also need to obtain an Electronic Travel Authorization (eTA) depending on their country of citizenship.
Hawai'i is a US state, therefore no passport is needed for US citizens to travel to or from Hawai'i. Hawaii is part of the United States. Therefore, if you are a Citizen or a Permanent Resident(Green Card holder) you won't be needing a passport to go there. DL will do.