Remote manage an iPad for a friend I need to help a friend who has an iPad. Talking live on Skype and sharing iMessages, even screenshots, is not cutting it. On a computer I can do with the likes of TeamViewer. 

This thread here on Apple.StackExchange offers some suggestions, but none of these apps like MobileIron etc do what I want: to control the screen of the target iPad, install apps, configure apps, etc. Just like TeamViewer -- full remote control. 

I am NOT looking for a corporate "profile management" type thing. I need to fully control iPad screen of a friend. 

Any recommendations would be super.
I'm afraid this is not possible, at least with a non-jailbroken device.
iOS Apps are built as SandBoxes at install time, which means that each App has access only to its own files, and very limited privileges with other of the device's services, such as the phone, sending emails, etc.
Apple states it like this:

For security reasons, iOS places each app (including its preferences and data) in a sandbox at install time. A sandbox is a set of fine-grained controls that limit the app’s access to files, preferences, network resources, hardware, and so on. As part of the sandboxing process, the system installs each app in its own sandbox directory, which acts as the home for the app and its data.
Important: The purpose of a sandbox is to limit the damage that a compromised app can cause to the system. […]