First of all, stamina can affect free throw in a sense that the player will be tired if he has a low stamina and he won't perform very well overall, hence affecting the free throw as well.
About training 2-3 weeks of stamina every season. In general, stamina drops 1 level down once a season, so if your players have good stamina, then training it once a season will be sufficient in my opinion (however, training 2 weeks will ensure that their stamina will stay at the same level or most likely increase).
The maximum stamina a player can have is 10 and in order to keep it at 10, one needs to train it every week. Ofc better the stamina, less drop in performance even after playing for a long time, so your players will maintain good performance, thus it will increase your team performance overall. But in my opinion, average/respectable stamina is sufficient.
The one drawbacks of good stamina is that a player will play for a long time, hence it can mess up the weekly minutes leading to drop in game shape. Lower game shape will reduce his level of performance, hence the team performance could possibly decrease.
So there are 2 sides. But keeping it around average/respectable/strong for all (or at least the starters) will be a good idea.