Because the ESTA application question appears just after the applicant has entered their passport info — which passport must be from other than the US — the phrase "any other country" means *any country other than the country which issued the applicant's passport*.

Unless someone weighs in on having had this exact experience, no one can guess if you'll be granted ESTA status or not. And even if someone has had that experience, there may be some difference in personal circumstances or travel history such that their "I got ESTA" might not apply to you.  

Your second question about a Green Card being seen as a "National ID" was answered by @phoog earlier [here][1].  


  [1]: https://travel.stackexchange.com/questions/148167/is-a-temporary-lpr-greencard-classed-as-national-id-card-for-travel