Can I run apps in a smaller resolution?
You can run su wm overscan LEFT,TOP,RIGHT,BOTTOM from Terminal (Superuser privileges needed)  

If you do not have Superuser privileges, you can hook your phone to a PC and run ADB command
adb shell wm overscan 200,200,0,0

For example, to achieve what you've shown in the picture above try running
wm overscan 200,200,0,0.  

But I must warn you, before running that, be sure you have USB debugging switched ON just in case overscan messes up your display, you can run
adb shell wm overscan reset from the PC connected.

WindowManager (wm) commands work on devices running Android 4.3 and above

May require a Reboot to achieve proper re-size.



Alternatively you can use Niwatori module if you have Xposed framework on your device.