no you do not
It depends where they are originally from.
A green card gets you into the US. It doesn't mean that you can use it to get into any other country! Each country you want to visit has its own visa regulations. Check these requirements at the...
If your visit less 180 days, no visa needed otherwise you need get a re-entry permit
Carry your greencard. Green card is required to board a US (mainland) based flight from Puerto rico.