1. If an American citizen were to take up citizenship in another country, must he or she give up his or her U.S. citizenship? If not, what are the conditions?
If you take up citizenship in another country, then the U.S. will consider you to no longer be a citizen. Incidentally, the same is not true the other way around. If a person of another country becomes a U.S. citizen then, depending upon the laws of the home country, that country may still consider her/him to be a citizen.