The radio should be connected to accessory so that it goes off with the key, but there is another connection that is to keep the memory set. Something isn't hooked up right.
As far as your lights, there is another thread where I just answered this in the past few days. You surely have a short, and from what you say, you have more than one fuse blow at a time. Correct?? Let me know, and I'll help you out some more.