The youngest president to die in office was President John F Kennedy.
That was Franklin Pierce whose running mate, Rufus King died before he made it to Washington .
William Henry Harrison was the first president to die in office. He died after a month in office.
Zachary Taylor was the second to die in office.
President Franklin Delano Roosevelt did die in office, in early 1945.
Nobody. A president continues to serve in office when he is impeached. If he is convicted and removed from office, the vice-president becomes president, same as if the president were to die.
JFK
Taylor
The sixth president to die in office was Warren Harding who died of illness, somewhat mysteriously , on August 2, 1923.
William Henry Harrison was the first president of the U.S to die in office. The vice president John Tyler took his place.
The first US president to die in office was William Henry Harrison who died in April, 1841. The president with the shortest term in office was also Harrison, and it lasted just 31 days.
John Adams