Yes
Barack Obama registered with the name Barack H. Obama at Columbia University.
Barack Obama is the only Columbia alumnus.
Columbia and Harvard.
He attended Columbia.
Yes he did, although it was called a college back then; he graduated from Columbia in 1983.
Barack Obama received a Bachelor of Arts degree in political science with a specialty in international relations from Columbia University.
Obama went to Columbia University, not Yale.
He received a Bachelor's Degree in Political Science from Columbia University.
President Barack Obama attended Columbia University and majored in political science. He spent two years there and graduated in 1983.
Barack Obama's current city is Washington D.C.
Theodore Roosevelt, Franklin Delano Roosevelt and Barack Obama.
I haven't seen any credible sources that mention he had a college nickname. In high school, he preferred "Barry" to Barack. But by college, he was using his birth name (Barack Obama) again. By the way, you may have seen some online claims that he was registered as a "foreign student" or that he was called "Barry Soetoro" at Columbia. Both assertions are false.