I am finishing my basement. How many 115 volt duplex receptacles/lighting fixtures can I install per 15 amp circuit?

There is no code restriction on the number of general receptacles in a dwelling unit... however you might err to the conservative to prevent overload, however unlikely...
Is this going to be a workout room? Be aware that treadmills can draw a whole circuit worth of power, so imagine what you may be plugging in and plan accordingly.

Generally speaking, I like to keep my lights on a separate 15 amp breaker.

For a garage, I would use a 20 Amp circuit and put GFCI protection on the circuit(s)