However, there is a 6 month window. So if Obama was adopted, he would have been required to affirm his US citizenship between Aug 4, 1979 and Feb 4, 1980.
He was at Occidental College during this period.
You mean the same Occidental College he may have entered as a foreign exchange student?
No, other way around. The person can give up his citizenship when he or she reaches 18, not affirm it. If they were born in the U.S. then their citizenship is a birthright that cannot be taken away from them, cannot be given up on their behalf while they are a minor, and cannot be relinquished by accident - the action must be deliberate. And there is no window for that. An adult U.S. citizen can give up their citizenship at any time.
You misunderstand it. If you're born a US citizen, you remain one until and unless you voluntarily renounce citizenship as an adult. Adoption does not change that.