Can I lock the functions on the touch bar? Is it possible to lock the touch bar to always display the default functions ("buttons")? I quite often use the buttons for sound and display brightness, but the touch bar almost never has them, since it changes according to my app on focus.

Basically, I want it to never change from what it would show as if it were physical buttons instead of a touch bar...
You can set “Touch Bar shows” to “Expanded Control Strip” in Settings - Keyboard - Keyboard.

You can alternatively leave it as “App Controls” and check the “Show Control Strip” box, which allows you to push the arrow on the right side of Touch Bar to show the expanded control strip.

Another alternative is to set “Press Fn Key” to “Expand Control Strip”, which will display the expanded control strip when you hold fn.