Could be a bearing, depends what the noise sounds like really.
Jack the car up and put your hands at 9 and 3 o clock and try to rock the wheel, do the same at 12 and 6 and see if there's any slack movement. If not then try turning the wheel and listening, if the bearing is bad you should hear it grind a little. Check both sides as it's often the opposite side from the one that it sounds like.
If it's a rubbing noise you hear check the wheel arches for silly things like the plastic arch lining having come away etc
Edit the above is for the turning left symptoms
as for the reversing issue it sounds like your car may not be engaging reverse properly, possibly a syncro issue although it could just as easily be a selector type problem, which is usually adjustable - this is potentially expensive so i'd insist it's rectified.