Hi, per subject - my Mac is on ethernet, but the same network (organisational network). I can do the safari test successfully on the iPad on the default port, but still no luck getting the application to talk to the mac. Not sure why - ?? I know you emphasise the need for WIFI, but the server test works yet still no connection?
If you passed the test then you are able to connect Actions, it is not important that part of your network is wired.
However your network is probably blocking Bonjour service, so you are not able to see your computer name in iPad network panel,
Go to Actions Server, Preferences > Network and have a look at the IP listed for your computer.
Then in your iPad open Actions, go to Network Panel and insert that IP pressing the field Custom IP Address.
If still you have issues have look at this article