Re: "The package system is broken" error - fgrlx related
I don't think this is anything specifically to do with the drivers. It's more likely due to that random third-party tool (which is completely unnecessary); I'm not really surprised it borked your installation, especially if you're combining that with the X-Edgers PPA. Without knowing what order you installed what, or whether you have installed the PPA version over the self-built version, it's impossible to know exactly what's gone wrong.
There is a line in what you posted which might indicate where an issue lies: "Uninstall will not be completed. See /etc/ati/fglrx-uninstall.log for details."
You might want to open that file and see what the error is.
Otherwise, if you like typing random stuff off the internet, try this:
Stage 1 - remove the fglrx driver
$ sudo apt-get purge fglrx ati-amd-v2.4-NoobsLab64.deb
$ sudo rm /etc/X11/xorg.conf
$ sudo apt-get clean
Step 2 - reinstall the fglrx driver from the repo
$ sudo apt-get update
$ sudo apt-get upgrade
$ sudo apt-get install -f
$ sudo apt-get install fglrx
$ sudo amdconfig --initial
Reboot.
1) ASUS GL702ZC: Ryzen 1700, 32GB, RX580, MATE@Manjaro-x64
2) Lenovo X230: Core i5-3320M, 4GB, Intel HD4000, Intel 6205, MATE@Manjaro-x64
3) MSI GT70: i7-3650, 16GB, GTX680M, MATE@Manjaro-x64