Chula Vista

First: The monolith on Jupiter (which is infinitely larger than the ones on the earth and moon) is the gateway to the Alien's home galaxy. The worm hole.

They buried the one on the moon because they rightly anticipated that by the time mankind had the advanced technology to discover it, they'd have also used that technology to develop weapons sufficient to destroy the Earth.

Second: Daisy was one of the first programs that HAL had implanted during his early stages of development. As Dave broke down HAL's memory he regressed back to being an "infant" and fell back on that early program. (a very sad scene in retrospect)

Third: Because he is Stanley Kubrick and that's the way he operated during his peak "mind f*ck" years.

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“The fact that we live at the bottom of a deep gravity well,
on the surface of a gas covered planet going around a nuclear fireball 90 million miles away
and think this to be normal is obviously some indication of how skewed our perspective tends to be.”