Everything Ffuries told you about your buttons is correct. Except, perhaps, the first two are actually the same version. The US Army first adopted the "Great Seal of the United States" for its uniform buttons in 1902. Until 1910, those buttons did not have a raised rim. Yours do have it, so they are post-1910. Then until 1923, the "Great Seal" buttons had what was called "black finish" on them because being shiny yellow brass color could reveal a hidden soldier's position to the enemy. There's too much gunk on yours for us to see whether or not there is any black finish on them.
Your button showing an eagle standing on a horizontal anchor is a 20th-Century "Fashion" clothing-industry crude imitation of the actual US Navy uniform button. A major clue about "Fashion" imitations is, the emblem lacks the crisp sharp detail seen on actual US Military uniform buttons. See the closeup photo of an actual US Navy button, below. Also, another ID-clue for actual US Navy buttons... note that the tops of the eagle's wings are sharp-pointed, not round-ish like on your Fashion imitation.
As Mud Hut helpfully pointed toward, your last button is not a Military button... but instead, is a Civilian-usage button from the very-early 1800s. Button-collectors call that specific type a brass 1-piece flatbutton. When that type has indented (not raised) lettering in the backmark, it dates from about 1810 into the 1830s.