I have upgraded my kernel using the RH network updater thingy.
Now my grub loader shows two versions of Linux (the old and new kernels).
Firstly, is this normal?
Should I uninstall my old kernel - if so how?
Or should I just edit my grub loader file to remove the old entry?
Does this mean that old versions of all the files I upgraded exist?
Yes your old kernel is still on your box. When using a new kernel, it is always a good idea to leave the old one on grub incase the new kernel does not work correctly.