Depending on the country and what state the other parent is, it could be really expensive. However, say if your child lives in Mexico, and you're in Texas, it would be feasible. If your child lived in say Japan, it would be really expensive and you would probably only be able to stage summer visits or something.
Yes, if it is a reciprocating country
I don't think so, unless the child was born on American soil (actually in America, an American territory, American military installation, or American embassy).
No.
Yes
If the president was an American citizen for more that 14 years, then maybe.
If you are an American citizen you don't need to do anything. He is all ready a citizen no matter where he was born.
If the foreign citizen is in the US and violates a treaty of the US, he/she can be brought in a US court. Otherwise, if the citizen is in another country, the court of that country is responsible for that violation.
If you were a US citizen and were charged with an offense in a foreign country, INTERPOL would no doubt have a record of it. Whether or not that INTERPOL record would then appear on your domestic US record, I don't know.
They are "Naturalized Citizens".
Naturalized citizen may be the term you want. Foreign-born is also used.
An American citizen can lose their citizenship by voluntarily renouncing it, committing treason, or serving in a foreign military.
Yes.