Indeed it does! Adoptive might be an alternative.
No, it does not. Whether a nation is someone's "adopted country" is a personal attitudinal decision, not a question of legal status. An immigrant could regard the country he migrated to as his "adopted country" before he is eligible for citizenship there. Just as parents of "adopted children" can also have natural children, so a person with an "adopted country" could still maintain ties with his country of birth, including citizenship there. He might be a citizen of both countries, of only the country he migrated to, or of only the country he migrated from.