Is it possible to freeze an app in Bluestacks? Sometimes is beneficial to "freeze" an application, for example when configuring on-screen controls for a game which doesn't display them at all times. Hotkey would be the most convenient.
What OS are you using? I'm going to assume Windows. I have no real experience with Bluestacks itself, but you can try suspending the whole process. To test if it can work open the Resource Monitor, right-click the Bluestacks process and click Suspend process. 

If it does manage to 'pause' the app you can work on making it programmable using perhaps PsSuspend provided as part of PsTools. Finally put it into something like AutoHotkey.

Usage:
pssuspend &lt;process name | process id&gt; (-r to resume)