All tools allow you to list the folders to back up. For instance, "Backups",
in the "System Settings" has "Folder to save" (in the left pane) and a "+"
allow you to "add" folders.
This is for a backup drive to save up space on.
If you then remove the original files, it is not a backup: it is just moving
files between disks! You can use the file manager to do so.
What commands can I enter in a terminal that would recursively remove all
video formats, disk image formats...etc ?
'find'. See 'info find' or 'man find'.
But you can graphically search files (and then remove them) too: filtering on
the name, the type, a maximal size, etc. That tool is in the default
Trisquel install (the package is "gnome-search-tool").