Turbo tax says my taxes were submitted and accepted. When I look at the file it doesn't have my return signed by me. Occasionally I get email updates asking me to finish?

When you e-file, it serves as you electronic signature. If you did not file your State with your federal, you may be receiving a reminder to complete your State returns. If your e-file status shows a status then your federal return was completed and submitted. 

The IRS expects to issue most refunds in less than 21 days after being accepted. Turbotax gives an estimated date based on the IRS's 21 day timeframe. So it all depends on the IRS and how fast your tax return moves along in the system. TurboTax does not receive any updates from the IRS.

For the most up to date information,  track your Federal refund on the IRS Where’s My Federal Refund? site.  You may also download the IRS2Go app to check your Federal refund status.

Continue to check the IRS tracker on a daily basis, as it is updated generally every 24 hours.