Battery Warning Light

You were not driving on the generator when the problem occurred. You were driving on the battery, and that is only going to last about a half hour. The multiple warning lights were due to the various computers shutting down from low system voltage.

What has most likely happened is the generator failed due to the bad battery. GM has had a real big problem with that since they redesigned their generators for the 1987 model year. GM generators develop huge voltage spikes that can damage the internal diodes and voltage regulator, and interfere with computer sensor signals. The battery is the key component in damping and absorbing those harmful spikes, but as it ages and the lead flakes off the plates, it loses its ability to do that. To reduce the high number of repeat generator failures, the battery must be replaced at the same time, unless it is less than about two years old.

Since you have the new battery already, the most likely solution is to just replace the generator. It is not practical to try to repair it. This one was not designed to be taken apart.

No. You are looking at two totally different systems.

The next thing is to determine why the warning light is turning on. Connect your voltmeter to the large output stud on the back of the generator in such a way that you can see what the charging voltage goes to while you are driving and the "battery" light turns on. If the voltage drops to less than 13 volts, the generator is quitting. If it goes real high, as in 16 volts or more, suspect a break in the fat wire going back to the battery.

How many wires are there in the small connector at the side/rear of the generator? There will be a brown wire. Are there any others?