Is it true that the apple has nothing to do with Adam and Eve?

Answer 1

Yes.

A) The fruit is not named. We do not know what sort it was, but it wasn't stated to be an apple

B) The disobedience of their action is what was at issue.

Gen 2:16 And the LORD God commanded the man, saying, Of every tree of the garden thou mayest freely eat:

Gen 2:17 But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.

Gen 3:1 Now the serpent was more subtil than any beast of the field which the LORD God had made. And he said unto the woman, Yea, hath God said, Ye shall not eat of every tree of the garden?

Gen 3:2 And the woman said unto the serpent, We may eat of the fruit of the trees of the garden:

Gen 3:3 But of the fruit of the tree which is in the midst of the garden, God hath said, Ye shall not eat of it, neither shall ye touch it, lest ye die.

Gen 3:4 And the serpent said unto the woman, Ye shall not surely die:

Gen 3:5 For God doth know that in the day ye eat thereof, then your eyes shall be opened, and ye shall be as gods, knowing good and evil.

Gen 3:6 And when the woman saw that the tree was good for food, and that it was pleasant to the eyes, and a tree to be desired to make one wise, she took of the fruit thereof, and did eat, and gave also unto her husband with her; and he did eat.