There. Fixed that for you.
one set of laws that covers how federal elections should be run
That would require an Amendment to the Constitution. For no good reason.
Not exactly. For presidential elections, yes, because the Electoral College is implicated. But for other federal elections, no. See Art. I, sec. 4, cl. 1: The Times, Places and Manner of holding Elections for Senators and Representatives, shall be prescribed in each State by the Legislature thereof; but the Congress may at any time by Law make or alter such Regulations, except as to the Places of chusing Senators (emphasis added).
Congress has the power of preemption of state laws on elections to Congress. But to implement uniform rules for presidential elections, yes, the Constitution would need to be amended.
Neutrinos have bad breadth.