How to determine which keyboard shortcut combo is free to assign? I've already spent much more time in finding a combination that works in every app (universal) than in creating the actual service. The shortcut triggers a service for increasing or decreasing the brightness of my external monitor.

I tried a ridiculous Control + Alt + Command + F1 / F2, but it doesn't work in apps like Finder, Preview etc. It only gives an error beep. (But is it already assigned? Or its portion is assigned and gets triggered?) I haven't found anything else since.

How do I find a free keyboard shortcut combo? Otherwise there's no point in creating them.
As @Tetsujin pointed out, 


  The beep doesn't mean 'oops, I've got a key conflict' it means 'the key command you just used has nothing assigned to it in this scope'.


After a restart, the (above) shortcuts worked in every app I tried. 

So after tuning your keyboard shortcuts, try to close and reopen the app in which it does not get triggered (beeps) or ultimately, reboot.

Also - there's no notification if you have an existing short cut and install an app that collides with that, so you may have to just remediate when an app or shortcut collide - defining another shortcut in that app to free your preferred use.