Selling players near the end of the season is beneficial financially as it brings more money; selling your players next season will bring less money because there is a significant drop in their market value. But, there is a risk you take if you sell players that are in your first team because next season you are not guaranteed that you will find a proper replacement on the first day (or even the first week). Also, there will be pressure on you to buy players on the first few days of the season.

I don't recommend to sell your players only to get a better draw in the cup. Take the challenge. Also, apparently, you will get more money as prizes if the level of the competition is higher.

The cup draw is done on the first day of the new season.