Such a thing does not exist: you either want a forum or a CMS.
Have you actually tried to browse this website's forums with your smartphone? It should adapt to it already.
Right now ---spam -- is made in Drupal 6.34. I want to shift it out of Drupal 6.34 to newer mobile friendly , responsive forum.
What myself and my programmer want to know is how to how to go about making an app for the latest version of phpBB , the challenges and the pitfalls in making and utilization of the app etc.
You are asking in the wrong place - you need to ask on a board where apps are developed to find out what is needed and then come back here with some positive questions.