The first Blitzball game can be won easily if you use Jecht Shot as soon as you can in the second half. But in order to do so, you gotta level up Tidus in the first half or else he won't be able to equip it for the second. Just get him shoot or pass back to someone. To ensure that the Goers don't score before Tidus gets the chance to shoot, get Letty, Botta and Jassu to pass between each other for the whole five minutes Which would level them up as well. When Wakka comes in, just try and maintain the lead. Use Venom Shot to stretch your lead a bit, if you want.

(SPOILER)Jecht wasn't really chosen to go to Spira. He just appeared there, disappearing from the Dream Zanarkand when he went out to sea for training. Tidus was brought to Spira BY Jecht because he wanted Tidus to kill him and bring an end to Spira. Auron knew this right from the beginning, he asks Sin at the beginning, "You are sure?"

So in summary, Tidus was brought to Spira to help Jecht.

(SPOILER)Shuyin was in FFX-2 and Tidus in FFX. So in reality, Shuyin was modelled after Tidus but I think you mean in the game's reality where Tidus comes from the Dream Zanarkand, a world that the Fayth of Spira had created. Whereas Shuyin came from the real Zanarkand, the one that had been destroyed 1000 years ago in the war against Bevelle. The Fayth were summoners of the real Zanarkand and in order to commemorate their fallen city, they recreated it in a dream state and modelled it exactly after the real one. Thus Tidus is the "fake"/"dream" version of Shuyin.