Skybridge beat me to it. If Hamilton's president now, I expect to see Shwarzenegger president by '92, even if we havn't annexed Austria by then.
Additionally, the seond-runner-up, Jefferson, should be vice-president. So that's two major amendments you haveb't told us about. Or is th POD the Constitutional Convention?
For your first question. Article Two of the Constitution states that no one but a natural born citizen or citizen at the time of the adoption of the U.S. Constitution can be presdient, which make's Hamilton's presidency entirley constitutional.
Why? Jefferson and Burr both received the same amount of electoral votes in 1800, and Burr become vice-president, did he not? The same thing happens here, except with the Federalists. Why is this entirley different?
You are thinking of this line: "Clause 5: No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President;". However, at the time United States would be interpreted by everyone- as it was intended- to mean a born citizen of Massachusates, New York, Virginia, etc. Hamilton was born in the Caribbean, not in one of the states at the time.
As for the second question, it is not different except in your version. The Federalists would not nominate Hamilton and Marshall- just Hamilton. And if Jefferson placed second, he would be VP. Marshall would only be VP if in a three way race he placed second, edging out Jefferson completely.