First point: Yes. The browser on my iPhone will allow me to type in straight IPs, including those on my own network.
In fact, as long as you can get a wireless signal that's connected to the greater internet, you can go anywhere a real computer can.
Second Point: It would look a lot like any other server farm: Racks upon racks upon racks of boxes with blinky lights. There would be bundles of cables coming from these racks to meet in central locations (logically at rows end, but who the hell builds 'em logically?) where small hubs and/or switches would be, and THOSE would have cables coming from them that would bundle over by a wall where the greater internet interface (read: modem(s)) would carry the signal off to parts unknown through telecomm lines.
Let me see if I can find a photo.