Is any full-time teaching position at any public elementary or high school at any US state
cap-exempt? How the fact of such exemption is established? How does the procedure of
obtaining a cap-exempt H-1B differs from a regular H1-B? What are particular advantages
and disadvantages?

According to the INS website
www.ins.usdoj.gov/graphics/publicaffairs/questsans/H1BChang.htm

In addition to increasing the cap, AC21 exempts H-1B workers who are employed by or have
an offer of employment from: • Related or affiliated nonprofit entity, or • Nonprofit or
government research organization.