After you file

There is no such thing as a direct deposit fee. E-filing is free, and so is having your refund direct deposited. If you choose the option to pay your TurboTax fees by having the fees deducted from your federal refund, you pay a refund processing fee of $39.99 ($44.99 in CA) to have a third party bank receive the refund, extract the fees, and send you the rest.

Check the status of your refund at IRS Where's My Refund or call the IRS.  If you did use the refund processing service, then the TurboTax help desk can look up your return and give you a status.