Something similar started happening to me shortly after i got the car, just not nearly as bad. It would happen when I loaded up the car, A/C, Headlights, Foglights and Stereo. I d get all the same lights you have. Turns out my crank pulley had completely separated in the middle and whenever stress was put on it, my alternator would stop spinning and my voltage would drop off. I drove a year and half like this because I was new to the Z. Needless to say during that year or so i replaced the alternator, battery, belt and connections to no avail. It was only after doing a 60k timing kit I noticed it. I couldn't get the timing light to find the marking to set timing. So i took it to a friend who is a Z and Skyline mechanic and he said hes never seen this before, then said ohh the pulley must be separated. Then he cautioned me to take it easy because it could fly off and kill the engine (I was driving it for over a year hard

). Needless to so I replaced it with a solid UR under-drive one. Never will have that issue again.