Will it still continue its execution in the background
For at least a few milliseconds, yes. Regardless of how an application moves to the background, once in the background, its process is eligible to be terminated, to free up RAM for other apps. When that occurs depends upon a lot of variables -- it could be milliseconds, it could be hours.
and will its priority be changed?
Background applications' processes run in a class that helps limit their CPU utilization.
Also, if at all the app uses higher amounts of RAM and CPU, is there any chance that the app will be shutdown by the android OS?
Regardless of amounts of RAM and CPU, the app's process may be terminated by Android at any point when it is in the background.