1) Does the cancellation of the I-20 has yes/no consequences for the student?
2) Can the student stay at the new school, with a cancelled I-20, but with his present valid and correct visa?
3) Does the student risk deportation if we continue at the new school?
4) Is he in any way in a illegal status right now or if he continues to stay in the USA with a cancelled I-20?
(1) Yes - once the Visa is cancelled - you are out of status and have to leave.
However, it is unusual for a Flight School to simply 'cancel' a visa if you are in good standing with that Flight School. If however, they felt you were not maintaining the required standard - or if you missed lessons etc - then they are within their right to terminate your visa.
(2) No - once your I-20 and therefore the visas in passport with the original School is canceled then you are out of status and must leave the US.
(3) Yes - most certainly. No visa then you are considered out of status and can be removed from the US.
(4) No - you need to leave the US and commence the process again to apply for a new visa and a fresh TSA submission.