I'll try to answer most of your questions, though I'm sure others will weigh in.
An At-Large bid is essentially an invitation to go. There are 3 types of bids. Paid bids get money to offset some of the costs, this is the highest type of bid. At-large bids and wildcard bids do not have any type of money. At-large bids are the middle level and get teams automatically to the 2nd day. Wildcard bid teams must compete the first day, Friday, to advance to Saturday where the 2nd and 3rd place wildcard teams will compete against all the teams in the division with at-large or paid bids. The 1st place Wildcard bid team from Friday automatically makes it to Sunday. Then the top however many teams (depends on the size of the division) advance to Sunday, regardless of bid type.
Yes, it really is at Disney World. ESPN is a massive sports complex on Disney property. There are no hotels attached, however the All Star Resorts (Sports, Movies, and Music), which are Disney resorts, are very close and many (most?) teams stay there. There is an option to stay off of Disney property though. The Disney Resort is really big itself, if you stay at one of the All Star Resorts, you are only 2-3 miles from ESPN. Anywhere else you stay will be further, especially if you are off Disney property. If you want to stay close at one of the Allstars I believe you have to book through the Summit packages, which your coach should be able to assist with. Another bonus of staying at one of the Allstar hotels is that transportation (buses) is provided for free to ESPN.