After having installed a new OS to an other partition, once started, the mouse cursor was good but I still had the messy display at non-native resolutions.
This time I knew, the AMD driver is not involved, so I went back to original installation and
looked into /etc/X11. I discovered there was no xorg.conf file, only two files named xorg.conf.fglrx-0 and .....-1.
I guess something did go wrong during the execution of amd-driver-installer-15.20.1046-x86.x86_64.run , so I did it again
this time stepwise (--listpkg, --buildpkg and finally rpm -i ...). I got a bunch of warnings during rpm -i but at the end I had an xorg.conf (identical to the xorg.conf.fglrx-1)
And after reboot, everything was fine.
My apologizes to AMD , the driver works (also with RHEL 6.7).