The type of application I want to build for ArcMap is to be run from inside of ArcMap and on a click of a button a custom form appears in front of User in which User enters certain parameters and then by some processing, the application returns resulting image to user in the same ArcMap Document... So will this application be an Add-in or Stand-Alone Application..??
Although if all your user needs to do is select certain parameters, you can probably accomplish this with a python script. You can then add that script to a toolbox and set the parameters there: ArcGIS Documentation
As for having a button that launches the form, you can accomplish this by customizing your interface and selecting your newly created python script.
The last part specifies that you want an image to return to the user, I'll edit this once you specify if the image is a raster (which would be added to the TOC) or an image that will be added to your layout.
Hope this helps.