Amidala dies of a "broken heart" on Alderaan while looking after Leia. I don't think she's assassinated or anything like that.
Why are the Jedi nearly extinct by Episode IV? Here's a thought: because of what Dooku told Obi-Wan on Geonesis, the Jedi are keeping a closer eye on the Senate than ever before. Maybe some kind of scandal happens where some delegates have their thoughts manipulated in one direction or another. It would be Palpatine's work, of course, but the Jedi would be blamed and accused of "subverting the democratic process". The Jedi are just banned from the Senate floor, at first. But Palpatine stirs up prejudice against the Jedi claiming they are behind the unrest in the galaxy and this will result in the Jedi being hunted down and destroyed.