1. Supposedly there’s a way to install nix without root access, but I can’t speak to it as I’ve never tried. Ofc it doesn’t require sudo to install packages or anything, though.
2. I don’t think it does this right now, largely because it’s super fucking complicated (as is basically everything Apple) and homebrew casks themselves have had a ton of headaches around it. But nevertheless, I think home-manager has some workarounds it uses itself to enable many common GUI apps on MacOS.
3. Not sure exactly what you mean, but I think it does that?

If you want to install packages purely by name, you can use nix-env -i hello or whatever. But it’s pretty janky and not really a recommended way of doing things.

Nix. I use it for everything, including all of my tools I use on my work MacBook.

There are many ways to use nix for this stuff, but personally I use home-manager in a flake-based setup. Versions of tools are all pinned in a lockfile which is committed to source control, so it’s easy to get my config and all my tools on a new machine without any breakage (it does require installing first, though).

It’s a great tool and has largely solved the pain of dealing with having to work on MacOS, for me.

Forced to use copilot? Wtf?

I would quit, immediately.