Yes, even you agree to give your ownership. The lender will not release your liability to pay the mortgage.
So you can either ask him to refi (as current rate is still low) or have an agreement with him to agree that you need to get monthly statement every month to monitoring the payment. when the mortgage is in default, you have some right to get the ownship and sale it. You know less than 30 day later does not affect your credit.
The answer to the 2nd question is no. Your credit may be affect. but the lender may not have right to get your other property if the property goes to foreclosure.