I might get a job as an ESOL teacher for fall semester in 2013 at a public elementary. If I have got a job, can I apply for H1B visa now, April 25th, 2012? Does academic institutions mean only for university not for elementary, middle, and high school levels? The only people who work for university are eligible to apply for H1-B Visa anytime?
No, everybody in public education can apply for H1B visas if the school is willing to sponsor you. Some websites show you which schools and universities sponsor educators like visalista.com or h1base.
Good luck!