My question wasn't related to reporting requirements. If you're in a country other than the US and a broker in that country offers accounts that provide access to the US market, where you're from originally is a secondary concern, I would think. There will always be reporting requirements depending on which tax jurisidiction(s) you fall under.
Not if you're American due to the global income tax requirement. Brokers may offer US markets trading but not to US citizens, even if they live abroad, because of the burdensome reporting requirement.
Not sure what is being asked. An American who travels to S Korea can certainly maintain all of his US brokerage accounts and be able to trade as long as the internet is not blocked. Certainly American needs to maintain a US address. American citizen would have trouble opening financial account with S Korean banks. He/she is considered foreigner.