What has Gene learned about hatred, jealousy, friendship and war?

Gene experienced each of these four things; what or how
much he learned will be up to you to decide.

Hatred -
Hatred is a form of jealousy, which is dealt with below.  The only hatred Gene had was
short-lived, but it had lasting ramifications each time it appeared.  In the moment when
he felt hatred for Finny's trying to subvert his academics, he jounced the limb.  When
he felt hatred for Leper's accusations that Gene hurt Finny intentionally (which of
course he did), Gene got physical with him.  Finally, when Gene is faced with the truth
of his actions in front of Finny in Brinker's mock trial, more hatred was shown, but
here the damage happens to Finny.  Gene learned hatred is a costly
emotion.

Jealousy - Gene was always a little jealous of
Finny's natural athletic and social abilities.  At one point, when that jealousy flared,
Gene committed an impulsive, cruel action which did irreparable harm to Finny.  He
regretted it soon after, and he learnedthat Finny was a genuine friend.  Gene learned
that jealousy, when acted upon, can be
deadly--literally.

Friendship - This is the major conflict
in this novel.  Gene at some point believedthe rather happy-go-lucky Finny was trying to
sabotage Gene's educational pursuits in order to make himself look or feel better.  He
was so sure, for that short time, that this was Finny's plan that he jounced the limb
and effectively ended Finny's life.  When Gene realized Finny was, indeed, a true and
faithful friend, it was too late.  Gene learned the value of a true friend and the
dangers of jumping to conclusions and placing his own motives onto
others.

War - The war was a steady drumbeat in the
background of this entire story.  It is real and Gene and his classmates all know
it--even Finny, who appears to be in denial--and spend their time preparing for it. 
When Leper enlists, The boys all get a jolt of reality; but when Gene visits the AWOL
Leper at his home, Gene sees first-hand the potential damaging effects of war.  Toward
the end of the story, he and Brinker plan to just enlist and get it all over with. 
Instead, Finny returns and those plans are dropped.  At the end of the year, when
Brinker's dad tried to convince the boys that "doing their duty" was a great and noble
thing, both boys believed it was neither great nor noble to serve.  Gene spent a year in
the service, but he never saw battle.  War was one of the growing up events of this
novel, and it's part of Gene's disillusionment.