The Question and Answer section for The Hunger Games is a great resource to ask questions, find answers, and discuss the novel.
One of the games had an issue with cannibalism. Hovercrafts are dispatched to remove the bodies as quickly as possible and make sure there is never a reoccurrence of this type of savagery.
In Chapter 25, as Cato holds Peeta in a head lock, Katniss realizes that she can't kill Cato without Peeta being dropped to the vicious dogs below.
The Capitol influences the games by changing the conditions of the game depending on ratings and audience preference. They will help or hinder certain characters to make the games more "exciting" as well as make themselves look good.