basement elecrtical wiring
The additional light... add up the rated max wattage of all light fixtures (including the new ones) on the circuit. If you have a dimmer, use this figure for the dimmer. If you don't, divide by 120 to get the amperage your lights will draw. This figure must be smaller than your wire is rated for (15a for 14awg wire, 20a for 12awg wire), as well as being smaller than your breaker rating. The short answer is that you likely can do it without any problem, but you need to check the numbers.
Your romex needs to be protected from a 1" nail and supported - the common way is to staple to the middle of the studs - more than 1.25" from the inside of the drywall.
The number of receptacles on a circuit is not limited by NEC, but for practical purposes, you probably don't want more than 10 or so. If you have a GFCI (either breaker or receptacle), it may have a max number of downstream devices in the directions - if it does, NEC says you have to honor that limit.