Ok, let's do some story background expansion! 

1. The grandmother gave the cup to the protagonist because she saw how happy it made her granddaughter whenever she saw it, and how the protagonist insisted on using the cup for all drinks whenever the opportunity came.
2. It was not a family heirloom at first, but as the grandmother gave the cup to the protagonist, it became a family heirloom.
3. The protagonist felt sad, as if a part of herself has been broken, since the cup represents in part the treasured memories she had with her grandmother. 
4. Yes, however, since the cup has a significant sentimental value, she decided to not let anyone other than herself fix it, despite it not being the smartest decision. 
5. As stated in the text, "The cup reminded her of her grandmother, and all the good times they had spent together. It reminded her of her childhood, and all the dreams she had for the future.", all memories she associated with the concept of love, hope, and happiness.
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