If you mean does he believe "there is no God but Allah, and Muhammed is his messenger"
I don't know.
If I were to venture a guess, I would say some of his beliefs may be based on what he learned as a child, which might be true Islamic teachings, some may be based on reading the modified versions of the Holy Quran.
No real way of knowing.
I do believe he considers himself Muslim.
I wonder if leaders in Muslim countries consider him a Muslim?
I’ve never believed that Obama is a Muslim, per se. I believe he’s a humanist/atheist, but that before becoming such, he was probably a practicing Muslim, though not at all fanatical or even much interested in it. I imagine he was immersed in Islam the way many American children are immersed in Christianity - it’s the relation of the parents, they go to church and participate in the rituals up to a certain age, but never really feel it. But I imagine he’s considerably more fluent in Islam than he is in Christianity.