DO I get charged processing fee if I pay with credit card?

No, there is no processing fee if you pay the TurboTax account fees with a credit card.

If you are referring to paying the taxes owed with a credit card, that is different.  There are fees as shown on the screen for entering your credit card information.

No, the processing fee is only for customers who elect to pay for their tax preparation and filing fees with their refund.