yes it can cause. TRhere might be two other things. The first one is that your tail lights wiring might have a short circuit and the second thing could be this that your tail lights buld might have fused or check the fuse box and check the fuse of your tail lights.
Well, check to see if you've blown a fuse or thrown a breaker. If the stereo is aftermarket and wasn't done correctly it is possible that it is the stereo causing you to have no tail lights.
May be. Crossed wires may cause short circuit. This short circuit might have done some damage to the internal wiring or the fuse of the lighting system.