1. Hal's name is supposedly derived from the "two systems of learning"; he is the heuristically programmed
algorithmic computer. Interestingly enough, though, Kubrick received an inquiring letter from a professional codebreaker, when the movie opened, who wanted to know if it was intentional that taking the next letter up from HAL produced IBM. Kubrick expressed suitable astonishment at the odds against such an occurence. Considering, though, that his last movie had been full of characters with names like Jack D. Ripper, I personally find it a much more likely explanation.
2. In this scene, HAL mentions becoming operational on the twelfth of January, 1992. I don't know about you, but I'm waiting on the edge of my seat.
3. Does the name Bowman intentionally imply heroism? Again, from the director of Dr. Strangelove I can't say it would suprise me much. The interesting question that raises, though, is what on earth does "Heywood Floyd" mean?
4. What we do get to look at here is a flashing red screen, with the words "COMPUTER MALFUNCTION" blaring across it as a grating alarm wakes up the less interested viewers. This always seems to me like a symbolic encapsulation of the entire Discovery portion of the film. "The computer isn't working. Wake up." Or maybe it's just a big idiot card for those of us having trouble understanding the plot. Whatever its purpose, I've always wondered whether Kubrick meant it to have a double meaning.