You can remove the 3.13 kernels. One single kernel is enough (assuming you
are sure it boots!). The package manager would prevent you from removing all
kernel images.
It is normal: by default, GRUB is configured to always use the latest kernel
image and 'sudo update-grub' is automatically run after you install such an
image.
The headers are indeed optional (and not installed by default, in Trisquel 7
at least). I think they are useless unless you compile modules for the
kernel.
I see no reason why the 3.4 image would stop booting.
It is not that painful: just search "linux-image" and click on the header of
the "S" (for "Status") column to get the installed packages at the beginning
of the list.
That is indeed normal behaviour. I do not consider that having my GRUB
configuration 'messed up'. My question still stands: in what way do kernel
updates mess up his GRUB configuration? Even though it runs an update-grub,
this does not affect the contents of /etc/default/grub, the primary
configura