You can test battery by putting voltmeter on battery before starting. 12.4'volts? Then hold voltmeter leads on battery while someone else is cranking engine. Does battery go below 10V? If so replace. If battery is good then what is voltage while car is running and leads are on battery (alternator test)?

Your battery light should not be illuminated at all while the engine is running. That said it means that combining your stated battery light being illuminated with your stiff steering complaint I suspect that the belt that turns the power steering pump; which is also the same belt that turns your alternator which would illuminate the battery light - I believe that this belt is broken, missing or very loose. Enough to reduce the alternator rpms and cause your issue. Some BMWS were recalled in 2009 for related issues.