You can use the black S Pen. There is no difference. Just the color of it is different. Make sure to buy the pen that goes with your tablet since they change the pen for different devices.
If the connection from the motherboard to the headphone jack is bad and it needs to be re-soldered, then you could fix it, but, if the actual headphone jack is broken (Fiio shows headphones connected, but no sound) then you couldn’t fix it without a new headphone jack. You also can’t get a new headphone jack online, so you would need to get a warranty. You can check warranty status here:http://check.fiio.net/. Also, there is info here: http://www.fiio.net/en/agreement