How to turn off screen without affecting anything else?
Depending on your kernel it might be possible to turn the brightness off your screen to 0 via t he appropriate sysfs file.

On a Sony Xperia Acro S currently running a custom AOSP-Based 4.2.2 ROM (SlimBean 6.2) i found the following:

130|shell@android:/ # find /sys/ -name brightness
...
/sys/devices/i2c-3/3-0040/leds/lcd-backlight/brightness
...


the following command turns my screen off but keeps the apps running:

echo 0 &gt; /sys/devices/i2c-3/3-0040/leds/lcd-backlight/brightness


if you combine this with an app which keeps the wakelock for your device, you should be fine.