can my employer require me to work 10 and 11 hr. shifts with no breaks whatsoever, as we are working by ourselves.

Yes. Breaks are only required by law for employees under 16 years of age. http://www.iowaworkforce.org/labor/iosh/consultation/wagehourfaq.pdf

I was told by my company in Iowa that I have to manage a certain number of hours for employees other than myself in order for me to go to a salary status. Where could I find this state law???

That doesn't sound like a state law, or a law at all; that sounds more like a company policy.

And if, by salaried, you are talking about exempt, here are the four classifications defined the the FLSA:
http://www.dol.gov/esa/regs/compliance/whd/fairpay/fs17a_overview.htm