How do I add a bank Debit card to pay for an item that I want to get?

There should be "Save for my next payment" checkbox under payment details form at the checkout.

But that's only if you want to "store", you don't need to add a payment card, because GOG has no continual payment or subscriptions.

I can't find the "There should be "Save for my next payment" checkbox under payment details form at the checkout."

I can't find any place to enter the debit card numbers, the date that the card expires and so on

See screenshot. You must click the circle next to Visa etc. then the boxes come up to enter the numbers.