How we cite our quotes: (Chapter.Paragraph)
Quote #4
Their goal was a still stranger world, almost twice as far from the Sun—across another half billion miles of comet-haunted emptiness. (20.15)
Hopes and plans here are like the signal TMA-1 sent out—they point out to the stars, in order to make you see the vast immensity of space. 2001 likes big dreams.
Quote #5
"You know that I have the greatest possible enthusiasm for this mission." (24.43)
Plans and goals tend to be seen as good things in 2001. The aliens' plans lead to the emergence of the humans we are today, and ultimately move us up the evolutionary ladder. Hal's enthusiasm for the mission, his single-minded devotion to the hopes and plans of Discovery, are a bit of a contrast. They don't end up leading anywhere good. (Trust aliens, not robots.)
Quote #6
It was even possible —though he had not yet looked into the supply position carefully —that by rigorous rationing he might remain alive, without resort to hibernation, until rescue came. (31.7)
Bowman is hoping he can manage to survive even after Hal has killed everyone else. Later, you learn that he won't be able to. You never see the process by which his hopes are dashed, but his impending death doesn't seem to disturb him that much. Bowman's hopes and dreams always seem oddly disconnected from his actual inner life; it's like the aliens have dreamed so much for him that he doesn't have any hopes left for himself.