Here is the answer to one of my own questions:

Three times in American history the Electoral College has elected a president who did not win the popular vote.

In 1824, John Quincy Adams, son of President John Adams, became president despite receiving fewer popular and electoral votes than Andrew Jackson, who finished first but failed to win a majority of either vote. Adams, after striking a deal with the third-place candidate, was elected president by Congress as required by the Constitution when no candidate wins an electoral vote majority. In 1828, Jackson defeated Adams handily.

In 1876, Rutherford B. Hayes lost the popular vote to Samuel Tilden by 247,000 votes, but won the Electoral College by one vote, 185 to 184. Hayes, who served one term, was derided by critics as "His Fraudulency" and "Rutherfraud."

In 1888, President Grover Cleveland won the popular vote by 90,000 votes but lost the Electoral College vote 233-168 to Benjamin Harrison. Four years later, Cleveland ousted Harrison from office, winning both the popular and electoral votes by a wide margin.