There needs to be 1L of fuel available for the FIA to test to ensure all fuel is within the regulations. Less than 1L won't be enough to properly test it.

Not sure if anyone has been disqualified from qualifying before but two years ago Vettel was disqualified from the Hungarian GP for not having enough fuel

No, financial penalties are exempt from the budget cap

Since he was disqualified and then allowed to compete in the race after a request from Alfa, my assumption is that he would start P20 no matter what