About the robot cart, Here is a VERY good design example if you want to make a custom one like you said, and meets all the requirements you stated.
http://www.chiefdelphi.com/media/photos/35516
This cart has
-tool boxes underneath the robot
-storage near the handle in the back (most likely for battery's)
-a place for the driver station
Now remember you have only 5 days till kick off, I would not attempt to start this right now but wait until build dies down. But instead get you shop and resources ready for Jan. 7th.