1:  The Windows/PB controls are transposed into the iPad/iPhone world by implementing the appropriate iOS controls. Will this process be fully automated by Appeon Mobile? 

Yes, this process will be fully automated by Appeon Mobile.  

2: For some complex PB controls that have no equivalent within iOS, how does Appeon Mobile transpose the Windows/PB controls into iPad/iPhone world?  

Appeon Mobile can transpose automatically all of supported PB controls. For the complex PB controls that have no equivalent within iOS, Appeon will design a set of cross-platform controls that will be run on iOS, Android, Windows Phone and other platforms.

3: Are there any properties/functions that Appeon Mobile cannot transpose automatically for some reason? 

  Only some properties/functions related with Mouse-move, Keyboard, etc.