It's tricky to give a reasonably accurate/useful answer without having more details on your intended integration, but going by what's suggested by "integration of Moodle features into our mobile application", I would recommend you start by looking at Moodle's capability as an LTI provider - https://docs.moodle.org/31/en/Publish_as_LTI_tool
Yes, most of the apis are ready through moodle webservices plugins, it provides you with the capability to create external webservices along with a built-in mobile service which you can use with their mobile app (open source also) the mobile app also has two version the first one built on top of phonegap and the second using ionic (and you can build it with phonegap). You can customize it as you wish and it contains all the necessary functionalities for having a course. You can also in the new version of it, to register as a new user.
And believe me, you don't want to reinvent the wheel, it's complicated and time consuming to think everything through, but if you want to spend time on it I recommend reading their code which is very beautiful and professional ( I learned a lot from this app as a developer).