What happens after a 5071c letter?

As long as you have done what they asked, you will just need to wait.

Once your return is filed, TurboTax has no control over the processing of your return or the release of your refund.

Here are a couple FAQs to track your refund:
When will I get my federal tax refund?
How do I track my state refund?
Why does Where's My Refund say "approved" but TurboTax still says "accepted"?

Thank you!  How long can that take?  It's going to be a month since I confirm my identity.  

Also - if an amendment needs to be made, will the IRS do it or will they notify me?