Can a WordPress site be converted into an iOS app? Maybe using something like PhoneGap to encapsulate the php?
If you wantto make a mobile app stay far away from WordPress. Many of the plugins and tools will become an issue when WordPress does an update an kills everything.
Phonegap is OK but not optimal. I suggest you create a web app using the M.E.A.N. stack. If you don't have the tech talent or budget, you can submit your project to an organization like www.AlchemyLab.co and their students can develop it as part of their projects.