Full remote access and control of iPhone from Mac, other iphone or other device without icloud
No, what you describe is simply not possible to do as a third-party solution in a non-jailbreak context. Apps installed from the App Store, or via other means, are run in a sandbox. They have no way of controlling the iPhone as a whole.
The only something like this is possible is by starting with a jailbroken phone, which basically comes with whole other can of worms.