Can I use iPad/Airport/Mac Mini as a development network?
A new Mini is most likely 'enough' computer, but you also have options as to which OS you run on it.  

Do you intend to run your development server on OSX?  You could also run Windows or Linux either natively or virtually.  Given the myriad options, I'm sure it's possible to do what you're looking to do.

Your AirPort will allow communication between the Windows PC and the Mini.

As far as the iPad goes, there's and app for that.  I've personally used the Teamviewer app and the RealVNC app.  Both have served me well.