That's hardly a little question!
Oh, I see! You finally get FFX, kain_ex! Congrats!

1. How you play blitzball TO WIN?
See the guide given by the game. You just have to score a goal like Football except this is in water, weird (Not ordinary) technique and 5 people instead of 11. And Tidus is a pig.

2. Where can I find massive amounts of Strength Spheres, Agility Spheres, etc.?
Monster Arena, that ogre monster (forget his name, you'll unlocked him if you capture all the monster in Mi'ihen), can give you spheres if you use a distiller on them (You can also use Extract Skill and auto-ability in some weapons). Monster in Macalania also gives some sphere.

3. How you get the Destruction Sphere from Zanarkand (if there's one, that is)?
After you have completed Zanarkand temple (I recommend you to do it after you have obtained the airship), return back to the temple and you'll see a white colour on the screen, step on all White Tetris and you'll found the location of the Destruction Sphere, take it and replace Besaid Sphere with it.

4. Monster's Arena worth doing?
You don't need to do this if you're planning to just win the game but I highly recommend you to do this since it's the main (hard) sidequest (like Via Infinito). Develop your skills here and PWN Jecht! If you have the PAL version, you can fight Dark Aeons.