*Since your original question had multiple parts to it, I had to edit your question down to one main topic (as requested by eNotes).
Chapter Eighteen in The Hunger Games makes a fierce contrast between the sweet innocence of Rue and the violent nature of the Games. In this chapter, Rue is speared by a fellow competitor, and Katniss, overwhelmed by emotion and her friendship for the young girl who reminds her so much of her sister, comforts the young girl in death and honors her body in death.
The theme of innocence in this chapter relates to Rue; her youth and innocence is sharply contrasted by the violence of her death, "a spearhead buried to the shaft in her stomach" (233). The ugliness and brutality of this violent act and the horrific violence of the Games is sharply contrasted by Collins' focusing on the tenderness of the moment shared by Rue and Katniss. Rue asks Katniss to sing, and while reluctant, Katniss fulfills her request, soothingly and and sweet, "the same songs [Prim] liked as a baby" (234). Katniss' song choice reinforces the childlike innocence of Rue, depicting her as truly a young innocent girl who had no place in the savagery of the Games.
Collins emphasizes her theme of innocence throughout the chapter as Katniss takes a moment to decorate Rue's body with flowers:
"I can't stop looking at Rue, smaller than ever, a baby animal curled up in a nest of netting" (236).
Again, the imagery of Rue as a "baby animal" further strengthens her depiction as an innocent caught up in the corrupt web of the Capitol's games. The natural imagery of the flowers that Katniss places on Rue's body also further strengthens the imagery of Rue as being innocent and untainted by the ugliness of the Hunger Games.
"I decorate her hody in the flowers. Covering the ugly wound. Wreathing her face. Weaving her hair with bright colors" (237).
Collins uses the bright colors of the flowers to challenge the morbidity of the Games and their violence. The peaceful quality of this scene between Katniss and Rue undermines the hostility of the Capitol's purpose in the Games. Later that night when Katniss dreams, her mind searches out Rue:
"Tonight it sends me Rue, still decked in her flowers, perched in a high sea of trees, trying to teach me to talk to the mockingjays. I see no sign of her wounds, no blood, just a bright, laughing girl. She sings songs I've never heard in a clear, melodic voice" (247-8).
This dream-like memory of Rue and her innocence helps Katniss cope with her own violent role in the Games; through Rue, Katniss can appreciate that goodness and innocence carry on, even if it is in only in her dreams.