My iPad is WiFi only and does not have a data plan. Also, most gyms we play in do not have WiFi. Does the app work without internet or wifi?

The app does not have to be connected to the internet while entering statistics. The only time you need to connect to the internet is when you run your first report so that you can register the app. Also, if you want to export (email) a report to someone then you will need to be connected to the internet.