macbook doesn't recognize internal HDD, only when connected via USB
It's probably the flex cable that connects the hard drive to the logic board. Some of the cables inexplicably went bad in 13" MacBook Pros--happened in my 2009 model. A new cable for my model was $9-$11 for the part at an Apple Store, and I got the tech to waive the labor charge since the part was so cheap. Looks like the cable for the 2011 models is $50 on ifixit (http://www.ifixit.com/Store/Mac/MacBook-Pro-13-Inch-Unibody-Model-A1278-Early-2011-Late-2011-Hard-Drive-Cable/IF163-026). Not a difficult repair at all if you're already out of warranty and would rather do it yourself, but use a nylon probe tool (black stick, can also be purchased from ifixit or elsewhere) to disconnect the battery from the logic board first and then carefully remove the cable connector from the logic board--don't want to break the logic board side. 

As far as overheating goes, the system will shut itself off or put itself to sleep if it gets above a safe operating temperature. If fans are running all the time, it could be something software related (runaway process, web video, CPU/graphically intensive app). If the fan and outtake vents are blocked with dust, could also be a lack of airflow. You can use compressed air (only hold the can upright) to blast out the dust when the bottom cover is off. Or if you take it to an Apple Store just ask the tech to clean up the dust.