How do I know a card payment really went through?

The reliable signal is in Orders — the order's payment status becomes "Paid" (the "Paid" filter tab). This only happens once the bank confirms the charge to Sellit. Open Orders and find the order: while it is in progress it reads "Awaiting payment"; if it failed, "Payment failed"; if it succeeded, "Paid". Pack and ship only once it reads "Paid". Remember: the buyer's "thank you" page is not proof — the status flips when the bank's confirmation arrives, not the instant the buyer returns to the shop.