The steering as above is well documented. A new battery may help as the motor does use a lot of power. However I installed a fresh battery a couple years ago and it didn't improve my steering. Some owners claim not to have the issue, but I wonder if it's sensitivity to the issue, i.e my wife doesn't notice it at all driving the car, but it's very obvious to me.
Your second issue could be the common gearbox bearing issue. Fortunately I don't have that issue, but I understand it only gets louder over time. The solution is to have the gearbox rebuilt with new bearings. Cheap parts but a fair amount of labour required so not particularly cheap.