If I understand you properly, you want to implement a REST API on the Yun, using the sketch and not getting into Linux programming. And then you want to access that API from the Edison. The Edison is the client making the requests, and the Yun is the server that responds to them. Is that correct?
If so, it sounds like the Bridge Example is what you need. You can find it in the IDE under File | Examples | Bridge | Bridge.
While the sketch as-is gives you basic pin level analog and digital I/O abilities, you are free to extend it as needed. The process() function is the top level API handler, and it decodes the first token in the REST request ("digital", "analog" or "mode".) If you want to add additional top level tokens, you would add additional if statements to this function.
Once process() decodes the top level token, it calls a function to handle the details of that verb. In there is where you would look for additional data in the URL to further refine the action, and where you would do the actual processing for the request.
So, to add more features, add a new "if" check to process(), and have it call a new command handler function.
Then, it's just a matter of making the requests from the Edison, and processing the results. You're on your own on that end, I have no familiarity with that platform.
Just keep in mind that you should be able to fully test your REST API from a standard web browser, by manually typing in the various URLs. I would recommend you implement the REST API on the Yun first, and test it fully using a web browser. Don't try to make the calls from the Edison until you know the Yun side is fully working. It's a classic divide and conquer strategy: get one side working fully before working on the other side. If you try to implement the Yun and Edison sides of the API at the same time, you will have trouble trying to figure out which side is at fault when you run into trouble. But if you have the Yun side fully working and testing, and run into trouble when trying to call it from the Edison, then you can be reasonably certain the problem is in the Edison side of things.