wgetis installedtaris installed
If you really don't want to install Nix under /nix (or you can't) then you can install Nix
in your home directory like in the homedir_install.sh script included in this Gist.
Now whenever you want to run a command under Nix's control, you should prefix with nixrun.
Good luck.
Link to proot is outdated:
proot-x86_64