I think one of the Team Eureka folks said the USB storage isn't available at normal runtime, but I could be mistaken.
Webserver is definitely possible, as that's what the Eureka Web Panel is, but general-purpose webserver use would be limited by both wireless bandwidth and moreso by the lack of storage (unless USB actually does work),
An important thing to keep in mind here... Unlike Android phones, tablets and TV sticks, Chromecast is much more scaled down and limited in design. I consider phones, tablets and TV sticks as Android-powered devices
with the qualification that they are meant
to be interacted with, apps installed, expanded, etc.
Think of Chromecast it more of an "accessory," black box or dumb terminal. Chromecast is more of an "extension" to those user-configurable devices.
Remember the ViewSonic AirPanel
it is a computer, but a very limited (embedded) one. While it mirrored the primary screen of the computer, rather than being a second screen, it's a similar model. The AirPanel has some intelligence to accelerate the user experience but the core processing is done on the computer it's attached to.
Neither AirPanel nor Chromecast are meant to be interacted with directly at the device level, or loaded down with a lot of background processes. Chromecast doesn't have an interactive UI of its own, nor does it have external input (keyboard, mouse, touchscreen, etc) like your typical Android device
I wouldn't surprised if a number of "standard" libraries that your typical Android platform has simply aren't there.
saying getting VLC on it is impossible - I really don't know, but I do think it's improbable
and would require a great deal of effort.
Without hardware acceleration or SDK/API support, you're relying purely on the software processing, and I haven't found much in the way of detailed specs on the platform itself. I have seen mention of the platform supporting other compression formats that Google isn't supporting yet, like MPEG-2, so it remains to be seen what Google's long-term plans are.
Not trying to be a downer here, just trying to keep things in perspective. After all, Google didn't sell us a $35 PS4 equivalent.