How can I figure out how many lights can be plugged in to one circuit?
Are the top and bottom circuits in a receptacle independent?
Add up the amperage of the lights (or wattage / 120) and check that figure against the circuit breaker the outlet is on.
No, they are the same branch of the same circuit. Well, 99.99999 times out of 100. It is possible to separate them by breaking off a joining tab on some outlet types, but I’ve nver seen this done in practice.