1. Why does Douglass believe that black service in the Union army will lead to an expansion of blacks' rights in the postwar world?

Douglass believed that serving in the army would ensure black people getting the right to full citizenship after the war.  

Explanation:

After the Second Confiscation and Militia Act that freed the slaves with masters in the Confederate Army, the abolition of slavery in the territories of the United States, and the Emancipation Proclamation, the black volunteers were still hesitant. It was black leaders like Frederick Douglass who urged them to become soldiers as a way to get full citizenship, as he thought it was meant to happen. In his own words, "Once let the black man get upon his person the brass letter, U.S., let him get an eagle on his button, and a musket on his shoulder and bullets in his pocket, there is no power on earth that can deny that he has earned the right to citizenship."

b. the right to wage war and make peace