I had the same problem with my 2006 BRV, the light came on whenever I went on the highway and accelerated. I went to the dealer and they said it was a software issue, they reprogrammed something and I haven't seen the red light since.
If the battery light comes on occasionally during acceleration or uphill driving, go to any GM dealership and ask them to look up a TSB on a Rendezvous battery light on issue. It takes one hour labor to reprogram the computer. If the light is on all the time, it's the alternator.
Its prolly a Charging system issue. Does the battery ever go dead? my best advice is if you have an autozone around they can test the charging system while its in the car. just hopes its not the alternator that requires tilting the engine forward and isn't an easy task.
replace the alternator
Normally the alternator is defective. It can also be a loose alternator drive belt, or defective voltage regulator.
the battery light means that your battery is being charged properly. so let it light.
You will have to disconnect the battery for 10 seconds or more to reset the computer, then reconnect the battery and check if the light is off and remains off , if the light comes back on I would take to mechanic and have it scanned for trouble codes.
If your engine is running , and the battery light comes on , that indicates that your battery is not being charged
Try an auto parts store, sometimes they will check your alternator and battery for free.
Replacing the battery should not have triggered the check engine light. The check engine light comes on when there is a problem with the emission system. Saying that, I would drive it for a while to see if the light does go out. If the light does not go out have the ECU scanned to retrieve the trouble code. Then use this code to diagnose the problem.
As long as the oil pressure light does not come on it will do no damage. If the light comes on, even for a few seconds, stop immediately.
Your battery is not being charged
Try to unplug the positive of the battery for a few seconds then put it back on(if your light comes back after a while then you should go to make it check)
Defective alternator or bad wiring.
if the transaxle light comes on in the car can you still drive it