I'd be careful. If you didn't cancel officially by letter and just stopped the DD and then go on to use your season ticket, then the club may be able to prove that you owe them back payments for the months you didn't pay them.
If you cancel DD, the club should know you have cancelled.
Well sort of, but it would require someone to correctly match the stuff happening at the bank with the sending out of the tickets. Not sure what system they'll have for that, but it could be quite manual.
If I cancelled my direct debit for my Car I'd soon know about it. They must surely have an accounts department.