Are these sentences correct:
1-I am sending in my short story for participation in the school competition.
2-I am sending in my short story for participating in the school competition.
If the sentences are fine, am I participating in the competition or "the short story"?
If you really want to use "to participate" then you could say "I am participating in the school short story competition". You wouldn't then need to say that you were sending your short story in, it would be implied. You couldn't really participate without sending them a short story.
You are participating in the competition.
You are competing (in the competition).
You are entering a short story.