What was the name of the United State's first spaceship?
If you mean satellite, it was Explorer 1. http://www.jpl.nasa.gov/releases/98/expl1rel.html
I am pretty sure the first battle was the revolutionary war. The American Revolution. before the American revolution United States was not formed as the United States yet. so maybe we have to apply that into this question and name the Battle of the bull run in 1861 the first battle of the civil war as the first battle of the United States.