Why the name "Fenway"? 

Constructed for the 1912 season, the new ballpark was named by then Red Sox owner John I. Taylor because it was built in an area of Boston known as the Fens. As Taylor said, "It's in that section of Boston, isn't it? Then call it Fenway Park."

Taylor, by the way, was also the person who changed the club's name from the Pilgrims to the Red Sox in 1907.

What is the meaning of that seat painted red in the bleachers? 

The seat in the right field bleachers is painted red to mark the spot where the longest measurable home run ever hit inside Fenway Park landed. Ted Williams hit the home run on June 9, 1946 off Fred Hutchinson of the Detroit Tigers. The blast was measured at 502 feet. Legend says that the ball crashed through the straw hat of the man sitting in the seat — Section 42, Row 37, Seat 21.