Because the ESTA application is asked by the US, the phrase "any other country" means *any country other than the US*.

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 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].