Banker told me it is possible to do dispute even if the card is not active anymore. So dispute could be done on already cancelled (reported as lost or stolen) card. How is this possible? As far as I am aware of, card that was cancelled (closed) cannot be used anymore. Dispute is still understood as "usage" so I am wondering how is possible to do dispute on already cancelled card?
A cancelled card means it cannot be used to make new purchases, it doesn't mean that you aren't responsible for the purchases before it was cancelled. Cancelling a card doesn't "clear the plate" of anything it was used for.
So take the scenario that your card was stolen at a bar just before you left. You went directly home and went to bed. You wake up in the morning, do things around the house, and in the afternoon head out. You notice now that your card is not where it is. You spend a few hours looking for it and then determine to report it lost/stolen.
In the 12+ hours your card was missing, the thief used it for numerous transactions. How can the bank know that those transactions are fraudulent, and the ones at the bar are legitimate? You have to dispute them. Otherwise the bank assumes all charges are legitimate up until you cancel it. Any charge after you cancel it (which is possible for a short time until the payment processing system updates) will (usually) automatically be discharged.
So the only thing you can do is to dispute a charge after the card is cancelled. You are otherwise still responsible for any charges on that card. Otherwise you could pull a scam, get a card, charge it up, and then cancel it. Cancelling a card does not remove your liability to pay the debt incurred.
Second question: The card is obviously attached to the bank account. If the bank account was closed by account holder, can be dispute of card unauthorized transaction still requested? Obviously I am referring to the card linked to already closed bank account.
This would only be "obvious" in the case of a debit card. Credit cards are not always linked to bank accounts. Again if you spend more than you have, this is the bank providing you credit. You are liable to pay that back, even if the account is closed. You can't expect to borrow a bunch of money from the bank, close the account, and not be responsible for the difference. When you close the account, it doesn't mean the bank "forgets you exist", if you had a fraudulent transaction and report that within a reasonable time, they will investigate it, even on a closed account.