A great big yes on all of that!
I have my own personal Medium publication so that I can already do most of the things that you describe. But that means I have to forego putting my writing in other, popular publications. It’s a trade-off and not always a good one.
I bring thousands of people to Medium from Facebook, Twitter, and Google every month. Literally. I’m sad that the three-article limit does not give those people more opportunity to experience Medium and decide to pay for it.