Suspect a big mess, but there is hope. Before you assume the generator has been damaged, there will be a very large bolted-in fuse that will be blown. All AC generators use multiple diodes which are one-way valves for electrical current flow. Those block current from discharging the battery when the engine is not running, but when the battery cables are reversed, those diodes become "forward biased", meaning they act like a piece of wire and in effect are a dead short. The extremely high current flow will blow that large fuse usually before it can damage and short the diodes. It is still possible one or more diodes are shorted, but don't assume that yet.
The dash warning lights tell you the computers for those systems are shut down. All computers have diodes built in that don't do anything under normal operation, but when the battery cables are reversed, they too become dead shorts and force the fuses to blow, thereby protecting the computers from very expensive damage. There are certainly going to be multiple blown fuses, so be sure to check the under-hood fuse box and the one inside. Also, a lot of import radios have a red ten-amp fuse on the back of the radio.
Here's a link to an article about testing fuses that might be of interest:
Friday, January 18th, 2019 AT 8:06 PM