As you've probably found, the 45th Division had a long and active service during WW2.
Regarding the medals, the Silver Star is a valor award. It is the third highest medal in the Army heirarchy of awards for actual valor in combat.If his discharge papers show a General Order number (often shown as GO#) you can get a copy of the GO from the National Archives, Modern Military Records Division in College Park, Maryland. Check www.nara.gov.If you don't have a GO number email me-- I might be able to get it for you.
The Purple Heart indicates he was wounded in action.An oak leaf on a PH shows a subsequent wounding.Thus if he had a PH with one oak leaf he would have been wounded twice.Two oak leaves, wounded three times, etc.
The EAME Medal was awarded to all soldiers and sailors who served for at least 6 months in the EAME Theatre.Each star represents a different campaign. If your dad had been in the 45th from the beginning, he would have had 8 campaign stars on his EAME.Five stars indicates, obviously, that he served in five different campaigns.
He should also have a WW2 Victory Medal, which was awarded to every soldier, sailor, marine, etc who served during the war.
As a combat infantryman, he was retroactively due a Bronze Star.In 1947 the govt decreed that any soldier who qualified as a Combat Infantryman was eligible for a Bronze Star.The soldiers had to apply for it, however.
You can write to the National Personnel Records Center in St Louis to get modern official copies of his medals. Expect a LONG wait. Alternatively, you can buy WW2 period medals on eBay or places like that.None of his medals would have been officially named to him.