Can I apply a surcharge only to payment by credit cards, and not to debit cards?

This is possible if your payment method can differentiate between credit cards and debit cards within the checkout process and makes this information available on Magento (ie. customers choose their card type directly on your website, rather than being transferred to a third party site to choose their card type and enter payment details).

If your payment method cannot differentiate between this, then different surcharges for credit and debit cards cannot be applied.