Does Turbo tax give you a expected date on your returns?

Once you're done filing they do but it's a very rough estimate. It lists the standard 21 days. You would do better to check your federal refund status by visiting irs.gove/wheresmyrefund. 

Yes, when you open your TurboTax Account, you will see the expected date of your refund.  You can also use our e-file status lookup tool to get your current status.