Since the first half of your question has been answered by someone else (see link below), I will focus here on "Half and Half," by Amy Tan.
There are two main conflicts in Tan's story: should Rose divorce her husband, Ted, and how should Rose's mother respond to the accidental drowning of her infant son, Bing?
Although Rose's mother had advised Rose against becoming involved with Ted, when the marriage between Rose and Ted begins to falter, Rose's mother advises Rose against getting a divorce. Paradoxically, the same values that had caused the mother to be suspicious of Ted now cause her to urge Rose to try to make the marriage work. Similarly, the same disregard for her mother's advice that had led Rose to marry Ted in the first place now makes her skeptical of her mother's advice to stay married. However, "Half and Half" does not, itself, tell us what the outcome of this conflict will be (we learn that later).
Rose's mother at first is hopeful that her son may not really have drowned; she hopes against hope that he may somehow have survived. When she eventually realizes that this is not the case, she loses her religious faith -- or at least seems to. Despite her apparent loss of faith, she keeps a small Bible propped underneath a table leg (supposedly merely to keep the leg balanced). However, when Rose one day looks inside the Bible, she describes what she sees:
On the page before the New Testament begins, there's a section called "Deaths," and that's where she wrote "Bing Hsu" lightly, in erasable pencil.
The fact that the name is written in "erasable" pencil, and the fact that the mother does not throw the Bible away entirely, implies that the mother may still feel some psychological and spiritual about the finality of Bing's death and about the relevance of religion to her own life.