That doesn't follow at all. Lead and copper aren't exclusive to South Korea. The authors get prestige and the owners of whatever patents are granted get some money.
Of course they aren't. But patent owners get to set the terms under which their patents are licensed. It's not like the record business where there is a fixed deal and if you use someone's lyrics you know up front what it is going to cost you. Someone might not even want to do business with you at all...
Yes, except that's the US government and the inventors here are in South Korea. I don't think the US would get away with declaring 'eminent domain' over something invented in a different country. They could choose to simply not honor the patent but that will open a massive can of worms, especially because a lot of this stuff depends on reciprocity: if your government doesn't honor our key patents, why should we do the reverse?
Carbon, oxygen, hydrogen, nitrogen, phosphorus and sulfur make up the bulk of organic molecules and plenty of those are covered by world wide patents (drugs).