If a bell is rung in a perfect vacuum and is suspended by opposing magnets will it ever stop ringing? As far as I am aware a bell rung in a perfect vacuum would only lose energy and stop ringing due to friction between the bell and the hanging mechanism (due to the lack of air resistance). Therefore would it theoretically be possible to suspend a bell between two opposing magnets or another suspension device that does not require physical contact and, when struck, have it ring forever?. 
There would be the issue of the bell moving to one side when struck, unless it was immobilised on all four sides by magnets. Would the magnetic force act as a dampener and stop the bell from ringing or would it keep ringing indefinitely?
 A: Internal friction in the metal of the bell eventually will bring the ringing vibrations to an end.  
The bell vibrates when it rings, making its molecules more energetic and creating heat.  Bonding between the molecules of the bell resist the vibrations, and eventually the strength of the molecular bonds will create enough friction to bring the vibrations to an end.
To address your 2nd question, see this account of a project to dampen machine vibrations by applying a magnetic field to a tool holder: http://dynamicslab.mpe.nus.edu.sg/dynamics/Project0506/thesis0506/Vibration%20damping%20using%20magnetic%20field%20boring%20process.pdf
It was found that a magnetic field will dampen vibrations of steel, which is both electorally conductive and magnetic, but is less effective in non-magnetic metals such as aluminum, and is  absent in non-metallic substances.  Interestingly, though it is theoretically possible for a magnetic field to dampen vibrations, most of the noise dampening effect achieved in the project was due to the mass of an electromagnet attached to the apparatus holder!
A: Anything that "suspends" the bell - whether it be a bolt, a piece of string, or a magnetic field - is applying a force. When the bell vibrates, this vibration will be transmitted. This is because the force of a magnet is a function of position - you can only get magnetic attraction because of a divergence of the field, so if you move, the force changes and this change will be "felt" by the magnet.
Obviously, this can be a very weak coupling - but it will be there. If you put a stethoscope against the magnet, you might be able to hear the bell - faintly.
"Ah!" you say, "what if we just send the bell into deep space, with no force acting on it and no pesky air molecules to slow it down?". Well, it can vibrate for a long time - but not forever. Any macroscopic mechanical vibration is subject to losses - usually, the friction of molecules against each other during the bending and stretching of the material in the bell will cause some internal heating. However, even a "perfectly" elastic object would experience some loss because the electrical charges that make up the atoms in the material are accelerating - and as you know, accelerating charges give off electromagnetic radiation. Now that effect is of course absolutely tiny for atoms in a bell moving at acoustic frequencies - but "forever" is a very long time, so we need to consider the smallest effects.
See also this earlier answer which addresses a very similar question.
A: Yes, it will end. When the bell rings, one side gets closer to the one magnet then the other. The other side gets further away from a magnet. This makes the force in one direction pull on the side as it goes back, eventually stopping the magnet. If we ignore this, then the bell will still stop, considering the force of gravity and how it stops all simple harmonic motion eventually. Also, the vibration will generate heat, and the heat energy will come from the vibration.
A: If it's suspended by a magnetic field, then ringing will cause a disturbance of the field. This will cause radiation of electro-magenetic energy.
The same is also true of the gravitational force the bell exerts on it's self. The ringing will cause gravitational radiation (loss) of energy.
Assuming that the bell is the size and density of a large black hole, the loss due to gravitational energy will still be to small to be detected. Loss due to electromagnetic radiation in a magnetic field, larger but still much smaller than losses radiated as thermal radiation.
