Battery warning light suggests the battery is nearly flat. I doubt there is enough power to drive the power steering motor, thus the steering is heavy (you're not just turning the wheels, but also the motor).
Whirring noise could suggest the alternator has had it, which means you've got a very little number of miles left available before the car runs out of electricity.
Stick your head under the bonnet and see if the auxiliary drive belt is still in place (assuming it has one), im not that familiar with what is driven by what.