Can android device issue adb commants to itself?
Adb is a two-part system, the "ADB" command that runs on your computer, and a daemon that runs on the device to receive the commands you send to it. 

To run it on the device you need a version of ADB that is compiled to run on the device. There are several of these on the play store (Search "Adb Shell") on Google Play, such as Adb Shell. 

There is also an "ADBLib" by Cameron Guzman on GitHub that can be compiled into an Android App and allow run Adb Shell commands from there.