Can I use another package manager other than Nix, such as AUR, dnf, pacman… other than Nix, or I cannot?
You can use distrobox on NixOS. You check the list of distros that can be installed as distrobox containers here.
Tell us a bit more about what you want to achieve.
If you just want to install packages with another package manager for no particular reason other than that you like the CLI of it better or something, just use its associated distro (perhaps with distrobox) instead of NixOS, there’s practically no way to do that. You can still install nix on other distros.
If you want to install a specific package you’ve found that isn’t in nixpkgs yet, packaging stuff if you’re using NixOS is hardly a barrier, especially with help from this forum.
If you’d like to do this because you’re trying to package something which is published as a .deb
and is otherwise proprietary or just hard to get artifacts for, nixpkgs does package some other package managers to achieve that.
… there’s probably a billion other use cases, I’ll stop guessing here. Tell us what you intend to do, then we can actually give good avice.