I was wondering what the President of the Senate's power were... does he have the power to bypass the Majority Leader - and is the Majority Leader even a constitutionally recognized position...?

The position of party floor leader is not included in the Constitution. It evolved gradually in the late 19th and early 20th centuries. The position developed separately within each of the major party conferences, with the conference chairs gradually assuming the functions associated with modern day floor leaders well before creation of the title itself. By the 1910s, both parties were electing conference chairs who acted as floor leaders, and by the 1920s, these leaders were exercising the full array of responsibilities associated with modern floor leadership.