Is your US Law Enforcement Safety Act (LEOSA) card recognized internationally?

Korea is heavily regulated. Sporting arms have to be stored at the local police department. Carry permits are based on demonstrated need and the approval of the local chief LEO. Those aren't commonly issued in a country where the police are normally unarmed and there is only 1 registered gun for every 1000 people.

In the PI, only citizens can own or carry guns.

No, It is not. Every State in the Union and Every Country in the World all have different Regulations, definitions pertaining to Law Enforcement and the Possession and Carrying of a Firearm. By either if you Are a Law Enforcement or Civilian.
The "Best thing to do," is to check with that Local Governing Body in which you want to go to visit or to Live, in reference to this question. Sorry if I wasn't all that much of help with this Question.
Good Luck in Your Ventures.

Most likely NO! HR218 is only reciprocal with the USA no where outside our country’s borders. Most governments outside of the US have strict firearms laws prohibiting carrying or possessing a gun. I would check with the US Embassy in each of those outside areas you want to visit. That being said, I’m still going to say NO with the above places unless you are specifically “on duty”, which it sounds like you will not be. Good luck to you!