How can I control my phone remotely? As a new Android user, this question has had me thinking quite a while. Is it possible to create an app or is there an app available that will do the following;


Remote access to your device 
Impossible to remove from your phone (rooting, flashing, w/e)
Turn your phone into 'Lost Mode' and make sure it can only be used remotely and disables all but the useful services to find your phone (camera, gps, etc)


OR


Impossible to remove from your phone (even after reinstall, etc)
Remains in the background whilst the person is using your phone as theirs (stolen, swiped and reinstalled)
Google's Android Device Manager service can do all of that apart from the remote control, though unless your phone has a new enough OS to have it installed by default (instead of pulled down as part of the Google Services updates) it's difficult to remove rather than impossible.


Find your lost phone with Android Device manager
Remotely lock Android devices