After a bankruptcy is discharged, can we turn the keys to the house over to the mortgage company before they start the eviction process?

Certainly.

Is the house included in the bankruptcy, if you go bankrupt and include the house, it is turned over during the bankruptcy.

If you file bankruptcy and don't include the house, then if there is money still owed though your loan, you can still be held liable. So have you discussed this with your bankruptcy attorney.

If you are going to turn the keys over, include the house in bankruptcy