“Their laws are meaningless to us unless we choose to go there.”
You are exactly correct.
Therefore, other nation’s citizenship laws are meaningless in the United States.
You have it exactly backwards. US law is binding on US citizens of which there are several classes. Naturalized, native-born and Natural-born.
Not if foreign citizens live on US soil. Those foreign nations will intervene on behalf of those citizens in certain circumstances.
Close, but not quite.
If you are born a citizen of another country, you are subject to those laws so long as you claim citizenship in that country (regardless of where you live).
Another country cannot impose citizenship on you. It has no legal authority to do so.
Citizenship is a privilege for people coming from other countries, not a right.