What questions remained after the Civil War was over?

The status of the freed people in the southern (and border) states was the principal issue left unresolved in 1865 at the close of the war. There was, in fact, the closure established by the complete Union victory and the Constitutional amendments outlawing slavery and making all people of any race citizens of the United States. After a brief period during Reconstruction when the federal government under Grant's administration did what it could for African Americans federal troops were withdrawn, and the southern states implemented Jim Crow laws to enforce segregation and oppression. This situation lasted for another 90 years.
Though not directly related to the war, two other issues in US life remained unresolved as of 1865. Unfair conditions of free labor continued to exist at least until unionization began late in the nineteenth century. And there was no closure or fairness in the treatment of Native Americans. The US army continued to fight an ongoing war with the indigenous people, and given that the Civil War was over, full attention was devoted to the completion of the transcontinental railway, accomplished in 1869. White settlement in the far west was accelerated, and within just over 20 years the last resistance of the indigenous population to the takeover of their land was defeated. With the situation of non-white peoples overall, the country had not fulfilled its promise of freedom and equality.

The end of the Civil War brought about an end to the attempts of southern secessionists, however, it also left open many questions on how to move forward as a nation. The country struggled with a number of questions that were not easily solved.
First of all, what was to be done with the leaders of the Confederacy and the soldiers who fought for them? Confederate President Jefferson Davis had led a rebellion against the United States. His soldiers had waged war against the federal army and killed its soldiers. A debate ensued over how they should be punished. Some wanted Confederate leaders hung as traitors. Others pushed for clemency in the name of peace and reconciliation. In the end, clemency was granted when President Andrew Johnson granted a pardon to anyone who took part in the Confederate rebellion.
There was also the question of all the newly liberated slaves. Four million African Americans were liberated as a result of emancipation. How they were to adjust to a life of freedom was a big concern. The Federal Freedman's Bureau was set up to aid in their transition. It provided education, food, clothing, and job training for hundreds of thousands of newly freed former slaves.
The military occupation of the former secessionist states was another question after the end of the Civil War. After the war and during Reconstruction the Federal Army occupied the former Confederate States. It was unclear how long they would need to be there in order to safeguard African American rights and stamp out any lingering secessionist tendencies. It was decided that the occupation would continue until the occupied states ratified the post-war constitutional amendments.