Please understand there is no rate that fits all people. It depends on what you qualify for.
With 10% down, Depends on whether credit score is 720+ OR 719 or below.
Assuming that you qualify based on full doc income, Best wholesale rates at this moment are 4.875% but you will be paying a mortgage insurance premium in addition.
Without knowing a loan amount it’s impossible to know the extra payment.
Rates can be different in a few minutes.
A lock guarantees your rate, but you still need to qualify.