HAVANA — Laying bare a half-century of tensions, President Barack Obama and Cuban President Raul Castro prodded each other Monday over human rights and the long-standing U.S. economic embargo during an unprecedented joint news conference that stunned Cubans unaccustomed to their leaders being aggressively questioned. The exchanges underscored deep divisions that still exist between two countries despite rapidly improved relations in the 15 months since Obama and Castro surprised the world with an announcement to end their Cold War-era diplomatic freeze. Obama, standing in Havana’s Palace of the Revolution on the second day of his historic visit to Cuba, repeatedly pushed Castro to take steps to address his country’s human rights record. “We continue, as President Castro indicated, to have some very serious differences, including on democracy and human rights,” said Obama, who planned to meet with Cuban dissidents Tuesday.