IANAL but doesn't the letter's language ("that termination shall become effective 20 days from today") imply that he has 20 days to fix things, and that the termination is not a already done deal?
"Cause" has meaning here. His days working for Uber are likely done but if he choose to rectify the issues stated in the letter then he might be able to get the terminated for "Cause" removed in which case he likely has some parachute clauses and payouts which can come into effect.
I don't know. If the court thinks there was a deal between Uber and Levandowski where they "fired" him for the duration of the trial, only to hire him back as soon as possible, that could lead to contempt of court charges, I feel. But IANAL either.
I'm assuming that since he's a high-profile hire from an acquisition with a lot of vesting cycles attached to it, there are more required legal procedures including time window to amend things.