Yes, a US permanent resident can work in Canada with the appropriate work permit or visa.
Yes, a US permanent resident needs an Electronic Travel Authorization (eTA) to visit Canada.
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.
You do not need a transit visa but a passport is required to re-enter the USA
Yes, they do. The Canadian permanent resident card is the only proof of identification that proves, both inside and outside of Canada, you are a permanent resident of Canada.
Yes, permanent residents of Canada can travel to Canada with a valid Permanent Resident Card or Permanent Resident Travel Document.
Yes, as a US permanent resident, you can travel to Canada.
The best known one is the Permanent Resident visa (green card) There are 2 visas in this category Conditional Permanent Resident visa (2yr green card) Legal Permanent Resident visa (10yr green card) Minor children have specific age related requirements with these visas. There are multiple visa categories that are used to enter US for the purpose of becoming a Permanent Resident & if you are in US legally on a visa that allows for Adjustment of Status to Permanent Resident, you will be able to file Form I-485 to petition for a Permanent Resident visa. The other work & school visas have restrictions on the length of time you may remain in the US.
Yes, permanent residents of Canada do not need a visa to travel to Canada.
No, permanent residents of Canada do not need a visa to enter the country.
The US has a visa waiver program under which nationals of selected countries are allowed to enter the US for periods of less than 90 days without a visa (you still need a passport) provided they meet certain other criteria as well. Permanent resident status does not make you a "national" of the UK; what matters is where your citizenship is. See the link in the related links section for more information. No idea about Canada.
Portuguese passport holders usually do not require a visa to enter Dominican Republic. A tourist card, however, is usually required to be obtained from your airline or upon arrival.