What is this huge opening right behind the gas tank? There are two of them, and I can't find a reference anywhere for a part to cover them. I could stick my arm through.

This is a spec racer and it just seems crazy unsafe to have 2 huge openings right behind the fuel tank right above my legs.

Your car is missing its air system. Those openings are for two of the vents.
Maddog Motorsports makes a kit of parts to close those openings.
http://www.maddogsmotorsports.org/accessories.html

I think Tangerine has them too.

Perfect! thank you!