Is there a way to keep full functionalities for those who have the app from before, while limiting the functioanlites for those who download the app for the first time?
No you cannot do that with the same app, since you have already rolled out a full featured app as free. What you can do now is you can take down your existing app from store(unpublish) and upload a new one with In app purchase capability. Hence existing users will not get affected and you will have a Free app which new users can download and upgrade to get more features. But by doing so you will loose reviews on your existing app.