1) I understand that in a case of sex with minors it is called rape no matter what. Is that even if it is voluntary, and no matter how old the partner is?
I note that RP pleaded guilty to unlawful sex, but not rape.
Legally, it's rape because the child cannot validly consent - just as it is if you spike a woman's drink (as indeed RP drugged Geimer) then have sex while she's unconscious: it is sex without consent, which is called rape. Polanski pleaded to a lesser alternative charge - in the same way that if you get in a fight and smash a bottle over someone's head, injuring them, it could (in English law, if I remember it correctly) be attempted murder, grievous bodily harm, actual bodily harm, assault, or probably a few other variations too (assault with a deadly weapon?). The prosecution might well let you plead guilty to one of the less serious options, rather than have to spend weeks of time preparing and arguing a case in court.

2) It seems to me that a bargain was struck, as is often the case, but not followed?
All the prosecution can do is recommend a sentence to the judge - it seems they did that, but the judge didn't agree with them that a few weeks of pre-sentence evaluation was sufficient punishment for the drugging and rape of a child. It seems current California law would require a sentence of at least fifteen years in prison, not six weeks, so the judge probably has a point there.

3) Why do the US authorites demand his arrest so many years after, and how do they even know he is there? And why do they do this when the matter is settled between the parties?
He's never actually served, or even received, the sentence for the original serious crime. What effect do you think it would have on pedophile rape rates if those convicted faced just six weeks behind bars when convicted? I would expect a lot of people to be outraged at such a lenient sentence.