I think the H-20 will be used for much the same roles as the H-6 is used today. Regular bombing, cruise missile truck, sea lane patrol, and yes as a fuel tanker. The main difference vs the H-6K besides the stealth will be its much higher endurance and range.
And no, it is highly doubtful that the designers of the H-20 will be the same as in the J-20. Xian has huge experience on its own in designing aircraft. They designed the JH-7 fighter bomber, the H-6K bomber, the Y-20 transport aircraft, the MA700 civilian airliner, and others.