I am not a big button person but the first on looks like som civil war buttons that I have seen and the second one looks like a ww2 button. No idea about the third one. I would good civil war buttons and see what comes up.
The second button is either a 1902-1909 Great Seal or a diplomatic one. I am leaning towards the Great Seal. I think your first button is post civil war, 1870s to 1890s. But these are just my guesses.
Your smaller button is a US Army enlisted-man's button made from 1854 to 1874. I cannot be any more specific about its date because the back is missing.
Your larger button is a US Army button made from 1902 to 1910. The version made from late-1910 to the present day has a raised border surrounding the emblem.