I see residency as the primary place where you live. What address is on your aircraft documents? Where is your "officail" mailing address? What address is your passport registered at? Where are you officially registered?
What is so difficult to define that?
As to operator. I see it as the main user of the aircraft, in case of many N-regs it could be the "owner". In other cases the operator would be the club, company, or other organisation that charters it out to others. Again, THEY are the ones with the paperwork showing it's basicall their aircraft, but they legally charter it out to pilots. They are probably also responsible for the up-keep, maintenance, etc.
So in my opinion, the operator is the person or organisation responsible for the aircraft.