iPhone going rogue--found SLAVE device and need help

Where did you get your screen repaired/replaced? I would restore the device to factory and not use a backup. That will clear your device, and you can then add your content back manually, without the backup from iTunes for music and apps. Make sure your contacts and calendar are synced with a program or service so you can get them back. Restore your iPhone, iPad, or iPod to factory settings - Apple Support

It is hard to tell about the software. I'm getting all sorts of hits in Google about it. Now that you have had a 3rd party open the device and replace the screen you will have difficulty getting Apple to support the device, since that work voids all support from Apple. I believe your best bet at this point is to restore the device to factory as I recommended, not using a backup, to remove whatever that is. I cannot find any match in the US App Store. I'm doing some more search at the Microsoft website.

I found this app for the iPhone in the App Store. It is a Microsoft Remote Desktop app, and it may be connected to what you are seeing. https://itunes.apple.com/us/app/microsoft-remote-desktop/id714464092?mt=8

Wherever you had the screen repaired they apparently installed spyware on your phone. Restore the phone using DFU mode and set it up as a new phone. Do not restore a backup, unless you have one made before you had the screen repaired.

DFU mode:

• Note that you must have a computer running Windows 7 or later, or Mac OS 10.9.5 or later
• Install the latest version of iTunes on your computer if it isn't there already
• Reboot your computer
• Disable any antivirus and firewalls
• Launch iTunes
• Connect the device cable to a USB port on the computer (not to a USB hub), but DO NOT CONNECT TO THE DEVICE YET
• Press and hold the HOME and SLEEP buttons at the same time for 8 seconds, until the screen turns black, then release the SLEEP button but continue holding the HOME button. If an Apple logo appears while holding both buttons you held for too long; start over.
• While still holding the HOME button connect the other end of the cable to the device
• You should see a message in iTunes saying a phone in Recovery mode has been detected (it may take up to a minute for the message to appear). When you see that message release the HOME button and the device should restore. When asked DO NOT restore a backup; set up as a new phone.