1) It really depends on the score, how quickly the pitchers are working in between pitches, etc. I would say count on at least 3 hours, but it could stretch out to 4 or 4 and a half hours. It could also be as short as two and a half hours, but normally games run longer than normal than shorter.
2) Sweet Caroline by Neil Diamond in the middle of the eighth inning. Take Me Out to the Ballgame in the middle of the seventh.
3) Anything you want at Fenway. The Italian Sausages are awesome, Fenway Franks (hot dogs), cheeseburgers, lots of beer, etc etc. It is VERY expensive, so bring a lot of money.
Have fun! It will be an awesome experience. Your English is pretty good.