Updating error

As long as you use newer versions (taken from Jxself's repository) of the kernel, the older versions will not be used by default because GRUB prefers the newest version (you can change its configuration or manually boot an older version from the "Advanced options" of GRUB's menu). Installing kernels you do not use takes useless space but does no other harm.

Do you actually want to use Jxself's kernels (has it helped with your brightness issue?) or would you rather go back to using Trisquel's default version?

Keep the newer kernels if they better support your hardware! If you added Jxself's Linux-libre repository (not a manual installation of one .deb package), then you will get frequent updates: only security updates until the version stops being supported if you installed "linux-libre-4.9" or "linux-libre-4.11" (in the latter case: the support will not last long!); also updates to brand new versions if you installed "linux-libre-lts" or "linux-libre". See https://jxself.org/linux-libre/ for more information.

Updates of the kernel (even mere security updates) eat up disk space because they do not actually substitute the previous versions. In this way, if the newer version does not properly drive your hardware (very rare) or even does not boot (I have never seen this), you can still boot the previous version. But having more than two kernels installed is only a waste of disk space (no other harm): you should remove the older kernels (all except the last one and maybe the one before, for safety) from time to time.

The "Synaptic Package Manager", in the "System Settings" is one user-friendly way to do it: search "linux-", click on the "S" header to have the installed packages listed first, select (Ctrl+click on the rows) all the packages whose names start with "linux-" and include a version number which is not the highest (or the second highest), right click on the selection, "Mark for Complete Removal" (an entry in the contextual menu), "Apply" (a button in the tool bar) and confirm the removal (in a window where you can read how much disk space will be freed).

You can indeed stop installing updates of Trisquel's default kernel too (version 3.13.0, in the case of Trisquel 7): you do not use it anymore. Just remove the related metapackage(s): in your case, "linux-image-lowlatency", which is the image (what takes most of the space), but you may have installed other (now useless) meta-packages that relate to Trisquel's default kernel ("linux-headers-lowlatency" for instance).

About your permission error, it relates to a file that does not exist anymore! Is the problem still present? If not, a reboot has probably solved it (somehow).

Both kernels are 100% free software (the blobs in vanilla Linux are removed). The main difference is the version: the older version, Trisquel's default, has been more tested but does not have the latest features introduced in Linux (in particular the latest drivers that support newer hardware). Different configuration of Trisquel's kernels ("generic'", "lowlatency", etc.) are packaged too, if you happen to have specific needs (musicians want low-latency kernels for instance).

Given the kernel you have, you installed either:

• the "linux-libre" package and will get really new versions of the kernel (not only security fixes) every two months or so;
• or the "linux-libre-4.11" and you are stuck on version 4.11 (which has a very limited support in time, i.e., you will stop receiving security fixes soon: this month!) until you manually install the newer version ("linux-libre-4.12").

The second option does not seem to make sense (manual work) but it allows to wait a little before jumping from one version to the next one. That said, for more stability (yet a more modern kernel than Trisquel's default), one can install "linux-libre-lts" ("LTS" means "Long-Time Support").

Again: https://jxself.org/linux-libre/ explains everything.

The user is "grub" and the password was randomly generated when Trisquel was installed. You can read it at the very end of /etc/grub.d/01_PASSWORD. Instead of learning that password, I suggest you to get rid of it... since it "only serve[s] to make it difficult to recover broken systems". That is what the developers of GRUB say:

By default, the boot loader interface is accessible to anyone with physical access to the console: anyone can select and edit any menu entry, and anyone can get direct access to a GRUB shell prompt. For most systems, this is reasonable since anyone with direct physical access has a variety of other ways to gain full access, and requiring authentication at the boot loader level would only serve to make it difficult to recover broken systems.
https://www.gnu.org/software/grub/manual/grub.html#Security

1. Open a terminal (emulator).
2. Open /etc/grub.d/01_PASSWORD (what requires administrative rights) with your favorite text editor (here GEdit):
   $ gksu gedit /etc/grub.d/01_PASSWORD
3. Add the "#" character at the beginning of all lines that do already not start with this character (or even delete these lines).
4. Save the modifications.
5. Make the configuration change be taken into consideration:
   $ sudo update-grub