LVM isn't "Linux Virtual Machine", it's "Logical Volume Manager". If I understand LVM correctly, to boot to a root partition on LVM, you need a separate /boot partition outside of the LVM (was that the small partition on /dev/sda2?). Your system may still have this, but if your FC12 installation overwrote it, recovery will be much more difficult.
Here's a couple of links to Grub vs LVM problems: link 1, link 2
Also see "Mounting a Linux LVM volume" -- you should be able to verify that your old FC9 system is still OK by mounting and examining its root partition while booted into FC12. If so, you can probably recover fairly easily, even if you've overwritten the FC9 /boot partition.
Here's an example Grub boot entry for an LVM system (source). In this case, (hd0,0) (meaning /dev/sda1) is a small /boot partition, and the rest of the system resides on an LVM on /dev/sda2. Note the root= and lvm2root= entries on the kernel line:
title Debian GNU/Linux, kernel 2.6.26 Using LVM with SATA Disk
root (hd0,0)
kernel /vmlinuz-2.6.26 root=/dev/ram0 lvm2root=/dev/mapper/sda_vol-root
initrd /initrd-lvm2-2.6.26.gz
Postmortem: This user ended up with the best-case scenario. The FC12 installation didn't overwrite or reformat FC9's /boot partition, /dev/sda2, and all that was needed was to access FC9's old /boot/grub/menu.lst and copy the boot entries into FC12's Grub menu.
1) An easy way to share files via right click -> share like in ubuntu & gnome/nautilus.
You can create a custom action in Thunar via Edit->Configure custom actions. Create an action to share a directory: net usershare add %n %f "" Everyone:F guest_ok=y && chmod 777 %f
And to stop sharing: net usershare delete %n. Make sure the command will show up for Directories only on the Appearance Conditions tab.
2) An easy way to browse through the network hosts and see the shared files also like in Ubuntu & gnome/nautilus.
Try pyNeighborhood.
Best Answer
Although this is an old question, I've found a solution by using the PipeWire technology with Gnome DE (in my case 3.32) and Chrome (at present version 77).
Check this out: https://wiki.archlinux.org/index.php/PipeWire#WebRTC_screen_sharing
Just open chrome://flags/#enable-webrtc-pipewire-capture, set it as enabled and restart chrome. You'll be able to share entire screen.
I hope it helps
EDIT:
As of 20 July 2020, since Chrome(ium) is currently using
pipewire0.2 whereas Arch Linux shipspipewire0.3, you also need to installlibpipewire02for screen sharing to work