The large button showing an eagle & shield is a version of US Army enlisted-man's button which was in service from 1875 to 1902. More specifically, your button's "HORSTMANN PHILADa" (note the small "a") means it was manufactured no ealier than 1880.
HutSiteDigger is correct, the button showing the letters GAR on its front is a yankee civil war Veteran's Organization button. The letters stand for "Grand Army of the Republic." The backmark "CUMNER, JONES & CO. BOSTON" date that button from 1879 to 1910.
The very small button showing an eagle with shield surrounded by stars is a 20th-Century reproduction of an 1835-to-1902 US Army Staff-Officer button, because it has a 20th-Century "self-shank" back.
Kuger is correct, the buckle with a long stud extending straight out from the center of its back is a "Conway buckle," primarily made for horse-harness, dating from the late-1800s to the present day. (You can buy them brand-new at horsegear shops.)
The buckle with a long oval-shaped brass loop at one end is a horse-bit harness "gag-swivel" buckle. If my recollection is incorrect, Creskol will probably speak up with the correct horsegear ID.
The group of discs with a ball-topped stud on them are "dressup shirt" collar-discs, dating from the latter 1800s into the early 20th-Century. See image below, from a 1909 Sears-&-Roebuck catalog, scanned by our fellow TreasureNet relic-ID helper BigCypressHunter.
