How to display external data using custom form in a Drupal page?
Not sure why you want to create a custom module for this, since ... there is a module that can "*display JSON results in a Drupal page" ... i.e. the Views JSON Query module. Some details from its project page:


  JSON Query is a Views 3 plugin that adds native JSON query generation. It allows you to parse JSON using Views' graphical query builder.
  It works much like Views XML Backend but with JSON.


And a screenprint from that same page:



For more details, read about it in the article about "Show external JSON data in Drupal Views".

PS: Similar solution if your input format is XML (instead of JSON), using Views XML Backend.