Here is a picture of my car's antenna booster. Mine had no reception for years. So when the panel was off for tint replacement I jiggled each connector until I found the problem. It is the antenna wire from the radio to the amplifier. I pulled it out and brushed it with a small wire brush and reinst...
Well the lighter is totally standard, I've used a few accessories there with no issue, including various USB chargers, so that's not why. Maybe there is some corrosion or debris in the socket? Try cleaning it out. Or you could pull the socket from a junkyard car and swap it in. I've probably got a s...