There are two questions here, so this response will address the second, about the state constitutional conventions of 1867 and especially 1868. These conventions were significant because they marked the ascendance of (in most former Confederate states) Radical Republican governments. By this point, the Southern states were divided into military districts, and states were required to ratify the Fourteenth Amendment. State legislatures, dominated by Republicans, called for constitutional conventions. Generally speaking, the constitutions they ratified established legal equality for African Americans, guaranteed them the right to vote, set up systems of public education, and rolled out other sweeping reforms. The right to vote for African Americans was required by Congress and was later mandated at the federal level by the Fifteenth Amendment.
In short, the constitutional conventions marked a brief experiment with multiracial democracy in the wake of the Civil War. As Reconstruction collapsed in Southern states, many of the reforms implemented in these conventions were rolled back, and many states called new conventions beginning in 1877.