You can do a search for him at this site:
http://www.sos.state.ia.us/search/index.html

and see if this individual is listed as a Not-for profit corporation. I'm assuming his business must be listed as not-for profit with the Iowa state if he wants to use the terminology listed above.

I know he is not listed as he has never filed any forms or applications with the state.

I know he is not listed there as he has never filed any forms or applications. So can he call himself non profit without any authorization?

No. In order to be a non-profit you have to go through a tons of steps to be come a 401(c)(3) tax status. If they aren't listed, they may be going through the process, but would have to file taxes until approved.

There are actually two types of non-profits. Each state has their own system for allowing you to file as a non-profit, however, this is not the same as a IRS recognized 501(c)3. Typically you file within your state as a non-profit and then you fill out the lengthy paperwork to get 501(c)3 status. I'm working on some right now for a group I volunteer with and I've been through this here in Colorado.

Note: My response is based on my experience as an auditor with the federal department of Health and Human Services. My specialty was audits of colleges and uviversities and nonprofit recipients of federal grants and contracts.

The primary advantage of a nonprofit entity is that they are generally not required to pay income taxes as there is no "profit".. I believe they must qualify as a nonprofit entity with the IRS and then file form 990 which reports their financial performance for a specified period.
Non profit entities are generally formed for income tax purposes and to shield investors from lawsuits.