I get 12.24v from the battery while the engine is off. I have red steering wheel light on with '!' symbol. It's very heavy the turn the wheel.
What car?
VW Touran 2003 1.6 FSI
It looks like that particular model uses electric power steering. It could be that the motor is going out on it. You can get underneath and check that the motor is getting power as it should. Hopefully it is not too hard to replace since you don't have to deal with hydraulic hoses and stuff.
I dont think the battery voltage will make the steering seem heavy. Maybe someone with more experience has seen this. Check the fuse as well as scan the car for any codes. If you have a light on the dash, it'll probably be accompanied by a code.
What is the voltage when the car is running? Unlikely the battery is affecting the steering. When the car is running everything uses power from the alternator.
It is between 14.11 - 14.22v when the car is running. I'm wondering if a battery change could make any difference.
No a battery change isn't going to affect it. You have plenty of voltage no need to waste money on that system. Bad power steering pump maybe.