Some people have his date of death on the 14th but like you said he died the next morning on the 15th which is his official date of death. Either way, a Republican President who was really really hated by a Democrat actor. My oh my, some things never change.
For all intents and purposes he was dead the instant the bullet entered his brain. His bodily functions simply stopped on Saturday. I doubt that he could have been saved if he were shot in 2015 and had all the advanced medical equipment of today . . . even if the machinery were right there in the box with him.