You can start with the execution of this command in a terminal:
$ sudo apt-get clean

It removes the deb packages that were downloaded (and that would only be necessary in the future if they had to be reinstalled). Then, you can remove, e.g., with the "Synaptic Package Manager" (in the "System Settings"), the older kernels: the packages "linux-image-*", "linux-image-extra-*", "linux-headers-*, etc. Just keep the latest kernel (with the highest version number) and, maybe, the one before that if you are unsure whether all your hardware is properly driven buy the latest version.

You can also consider the removal of programs that occupy much space. Typically video games.

But show us the output of this command too:
$ df -h

If you chose too little space for the root partition, you would have to expand it, probably at the detriment of /home... which has, by default in Trisquel, a filesystem that cannot be shrunk, i.e., you would need to backup /home first so that /home can be deleted, / expanded and /home recreated (and the respective line in /etc/fstab edited accordingly). But, you certainly are a serious user who does regular backups anyway, aren't you?

As for the Wifi, does it work when you are close to the hotspot? If not, it probably is not supported by Trisquel's kernel, which does not include any proprietary software (including firmware that Wifi chipsets increasingly require).

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