Quote 4
"I promise I'll come back in one piece," Denny said. She shook her head, which was still pressed against his body. "I don't care how many pieces," she said. "Just promise you'll come back." (14.15-17)
In this instance, it's not the distance that Denny is traveling that Eve is worried about—she's worried that she won't be able to keep the illness at bay when he's gone, and that she doesn't know how to fend for herself, taking care of a child and a dog alone, while also suffering this sporadic, crippling pain. She needs Denny, but she also promised she would be oaky if he left. So she has to keep that promise.
Quote 5
"No," Denny replied, and then, aware of his abruptness, attempted to explain. "I don't feel like company right now." (35.9)
Sometimes loneliness can be inflicted upon us, and sometimes we inflict it on ourselves, even if it's the last thing we want at the moment. Denny seems to use his self-imposed loneliness to think through things, to come to grips with his reality, and to form a plan for moving forward.
Quote 6
"Take it easy, kid," he says, pressing down on my chest to calm me. "I've got you." (1.15)
The language Denny uses here to describe Enzo, emphasizes how much he thinks of Enzo as not only a part of his family, but as a child. Denny, more than anyone else, raised Enzo. He's Denny's doggy son.