1) Once your CC is canceled, then the bank has no right to go after "new" government tax and annual fee. However the previous charged government tax or annual fee before cancellation if there's any is already built into your balance thus you need to pay.

2) Define corporate card. If it's a card issued by your company towards you under your name and the bill if borne by the said company, I don't think it will be canceled.

3) Usually for supp card application, the banks only access the primary card's holder credit history because ultimately the primary card holder is the one liable. But I can't confirm all banks or which bank does not evaluate supp card application's credit history.