Is it permissible to deal with an intermediary in online purchases without knowing whether the card he uses for payment is interest-based (ribawi) or not?

You are not required to investigate the type of the intermediary's card or to suspect the presence of usurious conditions, as dealing with it is not prohibited.

As for the intermediary's commission for using their card, there is no harm in it, provided that you give them the price of the commodity before the purchase. This would then be considered an agency for a fee, and you should not delay paying the amount to them.