Most of your questions can be easily answered by reading the game manual. You may also be interested in my FAQ thread.
Your controller will connect to the field via an ethernet cable, the other end of which will be connected to a piece of hardware in your driver station. If you’re interested, there’s lots of info about the field control hardware in this thread.
No form need be uploaded; the website will walk you through the process. From the robotevents.com homepage, click “VEX Robotics Competition”, then “Register a Team”.