It can do all but the third. Vim's understandably limited to displaying fixed size characters and so can't render webpages.
Hoover projects like Oni, Nyaovim or gonvim (All built on neovim) have the potential to change this (If they haven't already).
Neovim's UIs, yeah, plus you can (I guess) have a plugin that will open you a browser of choice in a separate tab or windowr, or pane or whatever with autoreload. This was done many times different ways before.
PS (this part was ment for a deleted comment):
I do agree that Atom's\Code's approach is friendlier of course. Still not an excuse for this kind of memory consumption, really. First and foremost this is a text editor. Making and assumption that the said text can't be more that a few Mb is stange.
I can open IDEA which is heavy Java IDE filled with so much functionality Atom can only dream of, and still - it won't eat more than 2-3Gb on a worst day.
So true, I almost posted a joke as a comment, only to delete it before actually commmiting a crime.
>Vim won't show me 4 panes with ES2016 in one...
I'm pretty sure most of this is doable though (not a Vim user)