>>697 #1, "Wrong English" - says that the "she" in question was given a good coach in return for winning the game.
#2, "Correct English" - doesn't sound right, should go down as "wrong.
I don't know the technical terms, but the problem is in the "for helping her".
#3, "Correct English" - best choice
>>702 "If you believed that this banana were a pen, then it would certainly be a pen" - best choice.
(It can also be written as "If you believe that this banana is a pen, then it certainly is a pen," but the first choice is better.)
Ken: "I guess I could write a letter using this banana"
or "I guess I could write a letter using only this banana," if the "only" is important.
"Only with this banana, I guess I could write a letter" - implies that the letter could only be written with that banana
in which case it should be "Only with this banana could I write this letter."