How can I fix my back wheel's wobbling? On my single speed bike--a POS J Fixie Cafe CF from BikesDirect--has an issue with its back wheel. The wheel wobbles 1cm back and forth when pulled/pushed from side to side. The freewheel has been making noises since the day I got it. The noises are KLINK! KLONK! every time I pedal. I believe that this is due to  a bit of a warp on the frame that makes the tire asymmetrical to the frame. Basically the left seat stay is slightly larger than the right one. (The lesson here is not to buy from BikesDirect, but go to a LBS.)

Anyway, what can I do to fix this? Do I need to get a whole new back hub? Freewheel?
A warped frame will not cause wobble when the wheel is moved by hand.  A warped frame can cause wobble when riding at speeds since the wheel is not straight.  However, if the wheel has play (moves side to side without rotating) in the frame, then the hub is not properly adjusted or is damaged.  

The noise issues could be from any number places and should probably be looked at as well.  

You are correct in the lesson, but perhaps not in the reasoning.  Buying from a LBS should ensure you are purchasing a properly assembled and adjusted bicycle.  Hub adjustments (like the issue you are describing) are one of the many build steps a good shop will perform when assembling a new bicycle.  It's part of why you are paying a higher price at your LBS instead of an internet warehouse with no overhead.