You can start to delete pachage caches, and see how much you gain... If not done often you can have a pile of old stuff. Check out the paccache arch wiki page for more info!
Pacman installs binaries in the root partition because they are installed system-wide. I don't think that pacman can install binaries for a single user (inside the home partition).
One way of achieving that would be compiling or downloading the binaries manually as a normal user and putting the .desktop file in .local/share/applications. The program would then be only accessible for a single user though.