Which MLB team has never won a postseason series?
Through the 2009 season, that is the Texas Rangers franchise. They have made the postseason three times and lost all three times to the Yankees.
Who was the First team in major league history to win a seven game postseason series after losing the first three?
2004 Boston Red Sox. The Red Sox were down to the New York Yankees, 3 games to 0, in the 2004 American League Championship Series. They went on to win four straight over the Yankees to advance to the World Series and then won four straight over the St. Louis Cardinals to win the World Series. The 2004 Red Sox are the only team in MLB history to have accomplished this feat.