I don't have skype installed at the moment but I do have Google Earth in my x86_64 system. The latter still works so far in my system after that. Perhaps you should start another thread for troubleshooting skype and Google Earth.
I also had "redhat-lsb.i686" with a few other i686 packages installed in my system to make Google Earth happy after its installation. I do not use Autoplus
as I want to learn how to make thing works myself. You could take the easy route to use Autoplus to install Skype and Google Earth for you.
Anyway, this is my suggestion if you want to do it the hard way. Open a terminal window then use "ldd" command to see which i686 shared libraries are missing in your system. For example, for Google Earth:
$ ldd /opt/google/earth/free/googleearth-bin
Based on your output, try to hunt down the missing libraries, if any. In my system this command produces result showing I have all the shared libraries. BTW, I keep in Gnote the list of packages I have installed back then. Here is the list after adapting to F17 to my best effort.
freetype-freeworld.i686 (if you are not using infinality