It no longer Matters.
Obama was an Indonesian Citizen which means at best he became a Naturalized Citizen. he is constitutionally Ineligible for POTUS, doesn’t matter if he was born on the Moon.
Probably, but if he's a Kenyan citizen that's a different story. Lots of people have dual citizenship from birth. Sometimes it's recognized by either or both countries, sometimes not. But in such each country claims the person as a natural born citizen. It would be true of any country which only requires one parent to be a citizen, or one, like the US, which bases citizenship on birth in the country, while the other uses citizenship status of the parents, like Germany, where Turkish (or other) guest workers cannot become citizens and neither can their offspring.
The US doesn't really recognize dual citizenship, but generally ignores the other citizenship, but not always. Traveling on the passport of the "other country" can be one of those cases, as can serving in it's military. But again, not always. Lots of Americans have served in the Israeli defense forces, and then returned to the US.