Quote 1
"The thing's hollow—it goes on forever—and—oh my God!—it's full of stars!" (39.20)
Bowman is wowed by the Star Gate. We would be too, understandably. This could be read as a description of the way Clarke sees sci-fi itself. It is vast, it is full of stars, and isn't that just shockingly nifty?
Quote 2
Yet still he called stupidly, as if an incantation could bring back the dead: "Hello Frank…Hello Frank…Can you read me?" (25.30)
Frank Poole's fate is probably the most traumatic, or unpleasant, death in the novel. Bowman calling out helplessly into the vast indifferent cosmos links the big universe all around to death. It's like he's floating alone in a big sea of mortality (though of course the aliens are out there to rescue him eventually).
Quote 3
"Unless you obey my instructions, I shall be forced to disconnect you." (26.35)
The best evidence you get that Hal is alive is that he's afraid to die. Death defines living—and where does that leave the immortal aliens?