My answers for Championships...
(P.S. you will meet tons of teams from outside the USA...)
1) Nope, there are so many teams with varying degrees of funding, they are spread out pretty well. You will need to go through this if you want to be anywhere in the area though:
http://www.firstchampionshiphousing.com/ (most hotels are sold out other than FIRST housing)
2) From what I have seen most FRC teams fly down on Wednesday, some even fly a portion of the team wed, the rest thurs, though with matches starting thursday this year, its probably better to get in before thursday if it works for your school/mentor schedule.
3) FIRST does the assignment for us. Usually its sort of like number order, ie teams 1, 2, 3, 4 go in Div A, B, C, D... but its not decided until a week or two before Championships (once nearly all teams have registered).
4) Smiles, spare clothes, soap, sunscreen...
On a more serious side, figuring out how to get your tools and batteries there is usually the toughest part. Some teams drive trailers down, some carry tools as checked luggage, some ship them down. Make sure you know the regulations (batteries cannot be brought on planes!!) and work with local teams to get your stuff down there. There will always be teams in your division that can lend you materials & tools, but having the basics you need to work on your robot and some spare parts (motors, assemblies, wires, etc) will make your life a lot easier. Oh and food prices are a bit up there, so make sure all the students bring enough $$!!
Congratulations & hope you guys have an AMAZING time!!
P.S. keep an eye out for 1511's Rookie Meet & Greet