Question: Is the "singing" by the monolith heard by the characters or just the movie audience?
Answer: As is the case with all non-diegetic sound in films, the characters do not hear it.
Question: Why did HAL go berserk? I thought it was because HAL knew the real reason for the mission (as Dr. Floyd reveals in the pre-recorded briefing), and was suspicious or curious of whether or not Dave and Frank knew. So when Dave is showing his drawings to HAL, HAL uses this opportunity to discuss the "rumours" with Dave. HAL of course is thinking as a computer in a chess game, and assumes to know what Dave will say next. But Dave thinks HAL is doing some psychology report on the crew and asks HAL that question. HAL did not expect this response, and quickly responds, "Of course I am." Now HAL is caught in a lie and does not know what Dave's next question might be, so he diverts the conversation by creating the AE-35 unit crisis. This, of course, sends the astronauts down a path that he cannot control, and he ultimately must terminate the crew to protect himself. 2010, however, went down some other path that did not make any sense to me. Hence the question. I would love the opportunity to discuss.
Answer: This is explained in the sequel, 2010. In that film, Doctor Chandra explains that Hal was given orders that directly contracted each other. He was informed about the monolith and instructed to complete the mission should the humans become unable to, but was also programmed not to deceive, and to relay information without distortion. This caused a "mental" breakdown in his programming. He decided the only course of action was to incapacitate/eliminate the crew and then complete the mission.
Question: Can anybody make out the instructions on the zero gravity toilet on the space craft?
Answer: The wording was spelled out in the "making of" book. Someone took the time to reproduce it here: http://www.ee.ryerson.ca/~elf/aso/zeroGtoilet.html.
Question: I don't understand the significance of the monolith or the starbaby. Can someone explain it to me?
Answer: The monolith is a monitor placed by the aliens to track the progress of developing civilizations. When humanity found the monolith on the Moon, that signaled a certain level of technological advancement. The starbaby is the evolution of the astronaut, as the symbol of humanity, from "Earth-bound" to a true child of the universe, turning his back on the Earth and looking toward the stars.
Question: What was the ultimate destination of the Jupiter mission? The giant planet is made of gas, it has no solid surface to land on. Theoretically a spacecraft could land on one of Jupiter's moons, but they lie within the lethal radiation belt.
Answer: The ultimate goal was to orbit Jupiter to study the Monolith also in orbit around it.
Question: Maybe I need to read the book, but can someone explain the whole ending sequence to me. Why all the flashy over dramatized pictures? It's artistic but is there some other meaning to it?
Answer: All the flashing images are supposed to represent Bowman travelling past far and distant galaxies, this is what happens in the book, where he travels to that white house place.