Basically what I want to achieve is if user checks chechbox saying: "Allow app to change your App’s Canvas URL and Secure Canvas URL within Facebook in order to work properly" to change these two fields on user's developer's facebook account. I haven't tried anything because I've researched a lot on Facebook Developers documentation and haven't find anything that suits my problem. I assume I'll need some of the permisssions to do this, but I don't know which. Samples of code would be very appreciated.
I did some research for you as well.
What you want to acomplish is possible. If found the right documentation on this page: https://developers.facebook.com/docs/graph-api/reference/application
You first need to have the Application ID and the app access token. HTTP example:
POST /v2.5/{application-id}?canvas_url={url}&secure_canvas_url={url} HTTP/1.1
Host: graph.facebook.com
I hope you can figure something out. Goodluck!