As far as I know, you can still download a plugin, install it in the plugin folder, and possibly restart WordPress, but it's a bit more risky. Installing a plugin via the admin interface is much more comfortable.

That said, as a WP admin of a tiny commercial website, I find it distressing that someone else can influence the functionalities of my Website. I already didn't install Jetpack because I dislike the intrusiveness and, frankly, the spying by Autommatic which is enabled by this plugin on our revenues and commercial transactions. All this points toward a direction that is not pleasant.

Yes. It's all just PHP. You can write your own plugin that does all this.

Not out of the box really. It's incredibly frustrating where everyone "rolls their own solution" for commercial plugins