How could I manage, that the morbo-server called here as a background-process will be shutdown/killed automatically if I close the Firefox-window or if I stop this script in some way?
#!/bin/bash
morbo Mojolicious_Lite.pl &
firefox -new-window http://localhost:3000/
OK, let's solve this one.
#!/bin/bash
morbo Mojolicious_Lite.pl & P=$!
trap "kill $P" INT # maybe you want EXIT here too?
firefox -new-window http://localhost:3000/
wait
This one should work... When firefox exits the shell will wait for remaining jobs (morbo) which then can be interrupted by Ctrl-C - in which case the trap kills them.
You can test it visually (i.e. seeing what gets executed) with
bash -x run.sh
Assuming your script is called run.sh ;)