How to list all files of a partition on linux?

find / -mount -type f -ls 

will list all files like with an output similar to ls -dils.

find / -mount  -type f -printf "%s  %h/%f\n"

will just print the size and the name.

The -mount (or -xdev) option tells find to not descend into other mounted file systems (which / usually has at least a few of) and type -f makes sure only files and not directories or links are listed.

See man find for more info.