In the book Night, what could Elie have done differently about his father's death?

While there was little Elie could have done to prevent his father's death, given how sick his father was, there was quite a bit that he could have done differently with regard to his reaction.

The text states that Elie did not pray or light candles (p. 106).  Both would have been acceptable; in fact, earlier in the book, the reader is introduced to the Mourner's Kaddish, a prayer said about, and over, the dead.  Elie did not have access to candles, but would have been able to recite the Kaddish had he chosen to.

Elie also did not cry.  He states that it "pained [him] that [he] could not weep," but concedes that he "had no more tears" (p. 106). He also admits that in some way, his dad's passing meant a greater freedom for him.  While he does not want to think that way, contemplating that freedom might have been some of the reason that he was unable to cry.  Thus, Elie has little to no outward reaction to his father's passing.