I can't even figure out how to install a stable version of Chromium. I only spent two minutes trying, but installing Chrome consists of one web search and one button click, so the difference is pretty obvious to me.
I believe it does, but I don't usually use it; rather, I usually get Ruby Version Manager to manage one or more Ruby runtimes on my Mac. Therefore I can't vouch for it to work with brew and/or brew cask.
Most of the more-or-less mainstream distros ship Chromium in their standard repos. In fact, they're more likely to ship Chromium than Chrome due to the fact that the former is FOSS and the latter is not.
Neither macOS nor Windows have such a philosophy of "prioritize the FOSS alternative", so Chrome is unsurprisingly the better-supported option there.
> Most of the more-or-less mainstream distros ship Chromium in their standard repos. In fact, they're more likely to ship Chromium than Chrome due to the fact that the former is FOSS and the latter is not.
That's actually how I first started using Chromium early in my Linux days; I didn't really know the difference between Chrome and Chromium, so I just picked the one that was easier to install. Once I finally learned the difference, I consciously made the choice to use Chromium on all of my systems, even the non-Linux ones.
http://macappstore.org/chromium/