I am currently waiting for my green card in the USA. I was wondering if I could travel to Puerto Rico since it is a territory. Under my green card application I'm not allowed to leave the USA, if I do it is seen as abandoning my application. However if the flight is domestic I assume there would be no problem as there is no immigration.
Flights to Puerto Rico are considered domestic flights, and US Citizens do not need a passport to travel between the US and any US territories. However, foreign citizens do need a passport to travel between the two, (see answers.usa.gov) so I can't say for certain how a trip like that will affect your Green Card eligibility. Your best bet is to check with an immigration official.
It's domestic, period, so no passport control. Never heard of CBP officials doing spot checks for flights to/from Puerto Rico but if they do, you could explain your Status to them in case you don't bring your passport. They will be able to check it out
Btw, once you get your Green card it's all you need even when entering the US from overseas. For example if you go to Europe, although a passport is needed for entry over there, once you get back to the US you simply present the Green Card.