Adding a new electrical outlet to lighting circuit
Am I allowed to add new sockets onto lighting circuit nowadays?


Yes.


  Do I need to worry about lighting per square foot?


Other than for your own personal preference since it's your own home, not really.


  Overloading the lights - well I only use LED lights, but someone in the future might stick something else in, right? What do I tell the inspector? I currently count at least 17 lights (14 of those recessed) on this branch (15A 110V), and like I said earlier, there are some sockets on this as well. I use all LEDs, but someone in the future might stick 100W incandescent bulbs in, overloading the branch. What does this mean for me.


The load is done as is installed. If you put this outlet in and later someone wanted to run a 5000W heater on it, that's still on them to ensure that they can, not the original designer. Since all of your lights are LED, you should very well be okay. It all depends on the wattage of the fixtures on the circuit and the overall load.