キャプテン翼, not キャプッテン翼;-)
2)
勝負をつける: to run off (the competition)
(In this context, the speaker uses it as "to win the competition".)
The target of つけてもらう is the players of other games than football in Nankatsu. もらう shows that the speaker (or students in the elementary school) receives favor from it.