I have an '08 Azera (which I mentioned in the comments). The Azera has a powered antenna, but not the electric kind which goes up in down. It's an antenna which resides in the back glass. It has a power booster which must be powered in order for the radio to pick up radio stations. In the Pioneer wiring harness, it should be a blue w/ white stripe wire (one which isn't used for anything else ... it should be marked as antenna, I believe). This needs to get attached directly to your cars wiring harness, as it appears the connector does not come with it. The tough thing to figure out is which exact wire this will need to be connected to. More than likely, all the other wires should be accounted for in the car side plug, so shouldn't be too hard to figure out.
Conversely, if your Sonata doesn't have the in window antenna, you won't need to worry about this wire. Tape it off so it doesn't short to anything and don't worry about it.
As far as adjusting the stereo as you stated in your last para, I believe this means you need to adjust the levels through the soft controls of the head unit itself. There should be settings you can play with to make things right with fader (front to rear/right to left). You should also be able to control the amount of boost the stereo puts out through these as well. If it sounds good after you get things hooked up, just don't worry about it (which is most likely what will happen, anyway).
