No Power Steering and Battery Light

[X5Moe4.4]

I'm not sure about the pre face-lift models but I know on the face lift models the alternator are water cooled, do you might be on to something suspecting that the alternator is the source of your coolant lose.

You can check your alternator by simply hooking up a multi meter to your battery while the car is on and measuring the voltage (I believe it should be around 14-14.4 volts while the engine is running).. If you don't have a multi meter, do a quick Google search on how to unlock your OBC and you can also read your battery voltage from the display in your cluster (again, not sure if you can do this in the previous face-lift models)

Our trucks act really funky when they don't get the power they need from the battery/alternator, so I hope your power steering issue is caused by just a faulty alternator.