Re: ABS and BAS/ESP dashboard lights.
First be certain the wheel speed sensor that was replaced is properly connected. There are two friction points when pushing the electric connector together in the wheel well. Be sure it is fully seated. Why was just the one wheel speed sensor replaced? A generic code reader will not distinguish which sensor is bad. You may have another bad wheel sensor.
You taking the correct steps to find a remedy, but with out a proper scan tool it is just trial and error. The Control Anti-Lock Brake, CAB could be a problem; they are not all that expensive and easy to replace. I believe you called it the ABS module in your post above.