Davers is correct... your button is an 1854-through-1874 US Army "general service" (non-Officer) button which has been hammered flat. Supposedly, that was done to use it as a poker chip. We civil war relic-diggers have found hammered-flat eagle buttons in yankee campsites frequently enough that it seems quite probable that that's what they were used for. (Often, several have been found in one hole.) I can't think of any other reason to hammer a bunch of eagle buttons flat. Note, they are indeed hammered-flat, not merely crushed by being stepped-on.
About whether it is a "2-piece" button":
All of the books on civil war buttons say the button's loop is not counted as a piece. See the diagram below, showing 1-piece, 2-piece, and 3-piece buttons, from the Albert book. However, at least one group of Archeologists, at the United Kingdom Detector Finds Database (UKDFD) does count the loop in classifying button forms.
Unfortunately, your fired bullet is definitely a post-civil-war one.