1) Has Jack's little hoochie daughter not been killed off or knocked up yet?
No, she was written out of the show and didn't appear in season 4 at all. They said that she and her boyfriend were living together happily but she never actually appeared. However, she is slated to appear in the show again this season (ugh, I can't stand her)
2) Why is Jack presumed dead this season?
He was forced to fake his own death at the end of the season in order to avoid being killed by a SS agent. The government was trying to kill him to avoid him being arrested by the Chinese government for an assault he lead on their consulate. The gov't feared that if taken he would talk and they would get blamed for what was a covert operation gone awry. However he was warned by former president Palmer and was helped by Michelle, Tony, and Chloe to fake his death, secure a new identity and thus the end of the season was him going off in this sense and everyone else thinking he had been killed.
3) Who's Michelle?
Michelle Dessler is a CTU worker who has moved up through the chain of command and was heading CTU by the end of last season. In season 2 she started dating Tony Almeida, in season 3 they were married, in season 4 they had become divorced but at the end of the season they said they were getting back together again.
4) What happened to the president?
President Palmer's term of office is over. He was followed by President Keeler. Last season Air Force One was shot down and the VP Logan stepped up in his spot. They never said officially that Keeler was dead, he was last mentioned as being in "critical condition" although anything I've read about the upcoming season mentions 'President Logan' so I assume they're saying that the VP has remained as president.
And hang on, when did you win the discus?