The regular season ends on Saturday April 19 (the last game you have scheduled).
The top 4 teams in each conference play in the promotion playoff. The bracket on your standings page is what the matchups would be if the season ended now.
The conference semifinal is played on Tuesday (April 22), and the conference final on Saturday (April 26). You can play a scrimmage on Thursday (April 24).
The league championship is a best of three series, with the first game played on Tuesday (April 29), the second game on Saturday (May 3). The 3rd game, if necessary, is played on Sunday (May 4). This is the only time, games are played on Sunday. Also, the game isn't scheduled until after the 2nd game is finished, so you might want to make sure you have a default lineup set, in case you can't get online. The Thursday (May 1) is available for a scrimmage.
The 6th place team from one conference plays the 7th place team from the opposite conference in a best of three relegation playoff series Tuesday (April 22), Saturday (April 26), and if necessary Tuesday (April 29).
The 5th and 8th place teams do not play in the playoffs. The 5th place team is retained in its current league, while the 8th place team relegates.
If you don't have a playoff game on the Saturday of the playoff weeks, BB will schedule a scrimmage against another league team for you. You can also schedule Thursday scrimmages. So depending on whether you are in the playoffs or not, you might only have two games for training minutes.
There is a transfer deadline just before the playoffs. Players purchased after the deadline won't be eligible for use in the playoffs. I think that it might be just before the final game of the regular season - but I'm sure it will be announced, and it also shows up when you look at a player on the TL whether they will be playoff eligible or not.
The draft list shows up about the time of the end of the regular season, so you have a couple of weeks to order your choices. The draft occurs the beginning of the new season (Monday or Tuesday) after the end of the season. Note: they have announced that the draft will be modified, so the above schedule is subject to change
Promotion/relegation occurs after the final is played. There are no Tuesday games for anyone that week, which is when the draft results are announced and teams are being moved to their new leagues, schedules generated, players aging, getting new contracts, etc. There is also an enthusiasm reset, and the game shape of players resets.
You will be able to play a scrimmage on Thursday (May 8), which could be considered a pre-season game, though it will actually be the last game of the training week that started in the previous season.
The following Saturday (May 10) is the start of league play in the new season, and the 2nd game is on Tuesday (May 13). The cup will start on Thursday (May 15).
So there could be 3 weeks in which you only have two games to accumulate training minutes, though playoff teams could have 3, so you might want to consider doing some team training (FT or stamina). And then the next week, you may have 3 competition games, where you may have to decide whether to play to win and not have good PT distribution for training purposes.