1.) No, you can register as an individual. You don't have to be in a squad.
2.) Yes, you fly both days. Basically two 'frames' are flown on each day. Each 'frame' lasts two hours.
The times were posted by Nash in a thread announcing Big Week a few days ago, but here they are:
Frame 1
» Sunday December the 9th, 2pm Eastern
Frame 2
» Sunday December the 9th, 4pm Eastern
Frame 3
» Sunday December the 16th, 2pm Eastern
Frame 4
» Sunday December the 16th, 4pm EasternIf you have any other questions, just ask.