Welcome to TreasureNet. The button with the eagle is known as a Great Seal (of the US) button, worn since 1902 by the US Army. Yours appears to have some remaining black finish to it, which was used primarrily during WWI, but up until 1924. The other is a collar disc, I believe from the NC National Guard dating somewhere between the world wars: Dating Metallic Insignia: Collar Disks
the rear attachment has broken off, but see the Type II discs in the link above
Nice finds, I think you US NC collar pin has something to do with the Cavalry, post WWI to pre WWII, your Great Seal button dates around the same time frame I believe, due to the black finish. The Experts will tell you for sure