Will I be charged a processing fee if I pay for TurboTax Premium with part of my federal refund?

Yes.  There is a $40 third party processing charge to use the option to have the TurboTax account fees paid from your federal tax refund.

Yes.   If you choose to pay your TurboTax fees by having the fees deducted from your federal refund, you pay an EXTRA $40 ($45 in CA) refund processing fee to have your refund go first to a third party bank.  The third party bank takes out your TT fees keeps the $40 processing fee for itself, and sends the rest of your refund to you.  You can avoid that extra fee by paying your TT fees upfront with a credit or debit card before you e-file.