Does Obama believe like these people?
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?