Yes, the lights and receptacles can be on the same circuit. I personally try to avoid that. No, the vent hood cannot be power from the appliance circuit, unless it is part of the stove itself.Is there anything in the code that prohibits placing lights and wall outlets on the same circuit? I know about the no other outlets on the kitchen small appliance circuits, but can the bedroom lights and outlets be together, living room outlets and lights, etc.
Another thing, on the kitchen small appliance circuit there is an exception for "Receptacles installed to provide power
for supplemental equipment and lighting on gas-firedranges, ovens, or counter-mounted cooking unit", does the hood/light above the stove count as "supplemental equipment"?(this is a gas stove btw)