What is the average time between initial application and closing for an FHA loan?
The correct answer is bettween 30 to 45 days pending on the customer, Lender and transaction.

I have a rental property I can no longer afford - what can I do given the market
I agree with Mike S.But also you may want to ask your renter to purchase the property.

Lock in rates
Depends on the lender policy - Read your lock agreement that was signed at time of your rate lock.If your rate has expired, typically it will be at worst case scenario.Current rate at the same lock window or locked in rate.Was the delay because of the lender fault or yours?