Who was the 1st republican president after 1850?
The US Republican Party had not yet been formed in 1850, so the first Republican President after 1850 was the very first Republican President : Abraham Lincoln.
Abraham Lincoln was the first president who was a member of the modern Republican party. Some sources, particularly simplified charts, describe earlier presidents as being republican, but that was a different and not directly related party, which was formally called the Republican Democratic party. Thomas Jefferson, for example, is often cited as being the first Republican president, but he was, in fact, a Republican Democrat.
No. The way our voting is set up, a vote for a republican president isautomatically a vote for the republican vice-president. To think of it in another way, we don't even vote for vice-president. We only vote for president and that candidate's choice for vice-president automatically becomes vice-president if that candidate wins the presidential election.