Once again Louie Turner has demonstrated an almost complete ignorance of the subject at hand.
The bronze star and bronze arrowhead you refer to are, in fact, small devices intended for wear on the suspension and service ribbons of certain campaign and service medals. The bronze star device is 3/16" in diameter and is worn to denote participation in a designated campaign or action; one such device is worn for each campaign or action with which the wearer is credited. A silver star device may be worn in lieu of five bronze.
The arrowhead device denotes participation in an armed, opposed landing - amphibious or airborne. In your father's case, this was probably an airborne assault landing. Only one such device may be worn on a particular ribbon, regardless of the number of assault landings an individual has participated in within the theater represented by the ribbon.
The U. S. government awards decorations to recognize heroic conduct and/or meritorious achievement and issues campaign or service medals to denote service within prescribed areas during specified dates or periods. None of these can properly be referred to as "hanging trophies".