Technical problems with Nexus 7 I have a one year old Nexus 7 and recently my tablet acts on its own. It starts to action commands without me doing anything. The only way I manage to recover control is to power it off and on again. This problem has become much more frequent in the past few days. 

I've a Kaspersky license and it hasn't brought to my attention any threats. 
Prior to having Kaspersky installed, I had McAfee Security, but I was never able to uninstall it because I can't deactivate its device administrator status. I don't understand why. 

What can I do to overcome these issues?
You should go to McAfee settings there is an uninstall option somewhere in the settings , on pressing that McAfee will ask you if you would like to remove it from device administrators , continue with the uninstallation from there.

And , for your immediate issue , I think your device has got a serious virus/malware or may even have been hacked , which is causing remote control by someone( I don't know if I am exaggerating a bit).

So firstly try killing all the network connections , manually remove  sim card (if your device has it) and turn off the Wifi router and then observe if those issues persist.

If issues persist factory reset your device , but prior to it take a backup of all data(or I think you should not because it will carry the malware with it so do accordingly).