There are external functions to interact with each module already. For instance, you can use the view_page external function to see a page.
If you cannot work all of that functionality in your app, why not fork it from moodlemobile2?
What you're talking about here seems to be single sign on. You could also consider signing into cas in your application and use cas authentication on your moodle. But I think you're trying to solve the wrong problem here.