OK, so if the whole senate votes on majority leader, do they also vote for minority leader? If so, why didn't the GOP elect Ted Kennedy to the role?
As I understand it, each party votes on their own party leader within their caucus, and then the full Senate votes between the two for the role of majority leader, with the loser of that election becoming minority leader.
Out of curiosity, why do they bother with the full Senate vote?
There haven't always been two parties. Think Unionists before the Civil War, the Farmer-Labor and Progressive Parties during their heydays, or the Era of Good Feelings when there were no real parties.
Each party elects its own leader and whip. The Majority Leader controls the agenda by scheduling debates and votes. There is a largely ceremonial position known as the President Pro Tempore which is generally held by the majority party's senior member (109th: Ted Stevens-AK; 110th: Robert Byrd-WV). The job of the PPT is to fill in for the VP when he is not presiding over the Senate. However, the PPT rarely presides over the Senate himself and usually appoints junior memebrs of his party to preside over the Senate so that they may become better aquainted with the rules. The job of the presiding officer is to announce vote results and call on Senators to speak during debate. Senate rules compel him to recognize the first Senator to stand up to prevent party favoritism.