The Player Search System is the evolution of the C-Gear and allows for you to interact with various players through local wireless or over the Nintendo WiFi Connection.
There are three levels of interactivity, Pass By which is for those you just walk by, Acquaintances which are those you interact with and Friends. Friends are determined from your 3DS friend list, and you're prompted after multiple interactions with the same acquaintance. You can have 100 friends.
In addition to that, you can battle and trade with people using the PSS. Trades run as normal, being able to pull Pokémon from the party and/or the box whereas battles allow you to have multiple rulesets and even select music as you start.
You can use Nintendo WFC with PSS, so yes, you can.