What is the longest amount of time that an inning of baseball has taken to play out? And what was the longest amount of time a baseball game has ever lasted?

Longest game time for MLB:

Nine inning game : New York 14 at Boston 11 4h 45m Aug 18 06
Nine inning post-season game: Dodgers 4 vs Washington 3 Oct 13, 2016: 4h 32m.
Extra innings game: Chicago 7 vs. Milwaukee 6 8h 06m May 08 84 (25 innings)

http://www.baseball-almanac.com/recbooks/rb_gmlg.shtml

Longest inning time -- 1h 8m -- On Saturday, May 8, 2004 in Arlington, Texas the Detroit Tigers met the Texas Rangers in a game the Rangers would win in the 10th inning by a score of 16-15. The 5th inning started with an 8 pitch walk, followed by 7 pitch walk, then a 5 pitch walk. By the time the top of the inning was over the Tigers had faced 54 pitches and recorded 8 runs. Being the home team the Rangers did not want to be out done, they faced 56 pitches and knocked in 10 runs. The entire inning saw 110 pitches, 18 runs and lasted 1 hour and 8 minutes, the longest inning in MLB history.

https://www.quora.com/How-long-does-1-inning-last-in-a-3-hour-baseball-game

The longest professional baseball game ever played was a 33-inning minor league baseball affair between the Rochester Red Wings and the Pawtucket Red Sox that took place on April 18, 1981, at McCoy Stadium in Pawtucket, Rhode Island. The two teams played deep into the frigid night with no end in sight. The game began just after 8:00 PM local time and continued until 4:07 AM the next morning, when it was paused after 32 innings. (The umpire's rule book was missing the revision that placed a curfew on game length.) On June 23, 65 days later, play resumed. The game was decided after just 18 more minutes as Pawtucket's Dave Koza singled off of Rochester's Cliff Speck to drive in Marty Barrett as the winning run, giving the PawSox a 3-2 victory. The official length of the game is listed as 8:25, also a record.

http://www.baseball-reference.com/bullpen/Longest_game_in_Organized_Baseball_history