Short answers, pulled from the story.
Since 2022, twelve teams qualify for the MLB postseason: three division winners and three wild card teams from each of the two leagues. The two division winners with the best records in each league receive byes to the Division Series, while the remaining four teams play a best-of-three Wild Card Round.
The MLB wild card was introduced in 1994 as part of a realignment that added a Central division to both leagues. The format was set for the 1994 season but the players' strike canceled that year's postseason, so the wild card era effectively began on the field in 1995.
There was no 1904 World Series because the National League champion New York Giants refused to play. Modern annual postseason play had begun only the year before, in 1903, with a best-of-seven series between the American and National League champions.
Since 2017, home-field advantage in the World Series is granted to the team with the better regular-season record. Before that, from 2003 through 2016, it was awarded to the league whose team won that year's All-Star Game, a rule introduced after the 2002 All-Star Game ended in a tie in Milwaukee, Wisconsin.
Since 2022, the World Series winner receives 36% of the total bonus pool, the runner-up 24%, the two League Championship Series losers 12% each, the four Division Series losers 3.25% each, and the four Wild Card losers 0.75% each. The pool is funded by 60% of gate receipts from a set minimum number of games in each series.
On the 23rd of July 2020, MLB and the Players Association agreed to expand the postseason to sixteen teams for that season. Eight teams per league competed in a best-of-three Wild Card Series hosted entirely by higher seeds, with the Division Series, LCS, and World Series proceeding as usual. The World Series itself was played at a neutral site, and MLB returned to the ten-team format for 2021.