paccache command is part of pacman-contrib package. Install it if you like.
Or use yay to manage packages cache…
# to see some statistics
yay -Ps
# to clear packages cache
yay -Sc
~/.cache directory
Usually, it contains files needed by some programs to operate faster, like web browser cache. I would recommend Qdirstat to investigate what is inside and eventually delete some files from here (At your own risk).
/tmp directory
is used to store the data used by the system and user applications to store the data that are needed for a short period of time.
It is managed by the system and cleared after each reboot.
Better do not touch by yourself