Ok let me give you a bit of advice that should help you immensely.
Abandon the REST methods. The REST methods were a game changer when they were released, and they were and still are very powerful. You can do anything you want with them, but we have better ways to do things now.
Encapsulate your logic inside an Epicor function. Then call the function via rest in your external program.
You can then inside the function, call the BO methods directly, and much more efficiently. You will also be less tightly coupled in your external app, as if functionality changes, you may only need to edit your function.
That being said, all the classic client stuff still works, so you can usually trace there. There are some minor differences where they have reworked a process sometimes, but for the most part it is the same.
If you insist on using the REST methods, I would use the V2 endpoints. You will need an API key for that. You will also need to use V2 to call functions.