Q. Assuming the citizenship changed while he was a minor, would he have had to reclaim it when he turned 18, or could he have done it at his leisure?
This line of thinking leads to some interesting questions. Did he ever "reclaim" it? Did he ever renounce the Indonesian citizenship? Is there any information in the passport/travel files, or in his college applications, or his SSN application files, with relevant dates?
What kind of information would you expect to find in his U.S. Passport files?
how and when did he change his name from Soetero to Obama after the divorce at which time he had his legally adopted name? Was it done legally in a court of laws, or just on a personal affidavit of some kind?
See my post above. There's nothing to reclaim, as he never lost his citizenship. It is virtually impossible for a minor, who's a US citizen, to somehow "lose" their citizenship, irrespective of who adopts them and what their nationality is.
Let me give you an example. Let's say there's a young boy who is Jewish and is born to two Jewish US citizens in Brooklyn. His father dies and he and his mother move to Israel where he is subsequently adopted by a nice Israeli man that his mother eventually marries. He is eligible for Israeli citizenship on two levels, as a "returning" Jew to Israel, and as the adopted son of an Israeli national and it's probable that his new parents would actually claim that citizenship for him, as would be their right as his legal guardians. But, through that entire process that young Jewish boy would never "lose" his US citizenship, and would never have to reclaim or declare his US citizenship at any time in the future, including when he turns 18.
And, as a clearly natural-born US citizen, he would be eligible for the office of the President. It's as simple as that.