One reason why I am using groups is to, as I said before, process the sum at once, like adding compressor to all vocals or the brass section. That means that I remove the input channels from the main bus, add them to a group and then add this group to the main bus. I can now also fine tune the sound with the EQ of the group. Things like this.
Monitor busses are handled completely different in my workflow. I use them to create a more or less independent mix, thats why they are called auxiliary busses.
You can use such busses for creating asignal for delay lines as well, but in most of the cases using matrices is easier to handle.simply send the main signal to one matrix and adjust EQ, level and delay.
I hope that answers some of your questions.
Just found this and I found it very helpful
This article does a great job of showing SQ signal flows
https://support.allen-heath.com/hc/en-gb/articles/4402940459537-SQ-Basic-Signal-Path-Diagrams-Input-Group-LR-Aux-Matrix