1. I'm fairly confident there is no amp. I think that was an early 90's thing.

2. Not quite sure what speakers are or aren't working in your car. You can use a 12v smoke alarm battery to test the speakers individually. If you have the polarity correct the speaker should pop up I believe, if it's reversed it will pop down.

3. No problem at all, I did this. Only the two positive leads go to the fader from the rear speakers. The negatives for the rears and everything else you need should be behind the headunit already. I believe the wires you need from the fader are Red/Brown and Gray/Brown. Again you can use the battery to test this.

4. You shouldn't need to rewire anything, just cut off the fader and pull the wires back to your head unit.