GNAT is part of GCC, I'd look in your package manager for "Ada" and/or GCC.

I'd recommend asking in https://gitter.im/ada-lang/Lobby

I don't think so, last I checked you have to download the graphical installer from AdaCore. I'm not sure why it's this way.

I've never had any trouble with the installer, at least.

Alire (https://alire.ada.dev/) can do the toolchain install now. It's pretty much like cargo, and can also be used to select from multiple toolchain versions.