What are parallelisms and what examples are presented in the novel The Great Gatsby by F. Scott Fitzgerald?i have to write an essay in which I...

Well, grammatically, parallelism generally refers to a
sentence structure which "matches," so to speak.  For example, "The young girl was
interested in gathering flowers, pressing them
in books, and using them for her scrapbook work."  This
is not parallel structure:  "The young girl was interested in
gathering flowers so she could press them in books and then use them in her scrapbook
work." 

The tone of your question, though, implies the use
of parallelism in a broader and biographical sense--as in ideas or things in the novel
that are parallel to or matching Fitzgerald's real life.  If that's the case, it will be
an interesting study for you, because much of what happens to Jay in The Great
Gatsby does parallel the author's life.  Here are a few to get you
started:

1. Both of them were born into lower
   economic circumstances and managed to work themselves into
   affluence.


2. Both were fairly disillusioned by the
   excessive lifestyles of the rich during the '20s.


3. Both
   had their hearts broken by the fact that they weren't able to marry the women they loved
   when they wanted because they didn't have money (though, unlike Jay,  Fitzgerald does
   marry Zelda eventually). 

That should get you
started, anyway.  There really are a lot of parallels which your research will reveal. 
If you're interested, I'd also recommend a Fitzgerald short story called "The Sensible
Thing" (which I've noted in a website for you, below).  The main female character is
Jonquil (also a flower name, like Daisy) and the protagonist is even closer to
Fitzgerald's real life than Jay Gatsby,  It may or may not be helpful to your research,
but it will give you another view of parallelism between the author and his work.  Hope
this helps!