The lowest temperature a superconductor can work at is generally close to absolute zero, which is -273.15 degrees Celsius or 0 Kelvin. This temperature is necessary to achieve zero electrical resistance in superconducting materials.
No, only certain materials can become superconductors. These materials form Cooper Pairs with their conduction band electrons at low temperature, making the electrons coherent (analogous to photons in a LASER beam). This coherence prevents resistance to current flow. Most insulators lack conduction band electrons. High temperature copper oxide ceramic superconductors are an exception as they lack conduction band electrons, but their copper oxide structure is highly distorted in a way that allows bound electrons to form Cooper Pairs.
Fullerenes are molecules composed entirely of carbon, arranged in a hollow sphere, ellipsoid, or tube shape. They have high heat resistance, are excellent electron acceptors, and have potential applications in nanotechnology, biomedicine, and electronics. Fullerenes also possess unique electronic and chemical properties due to their hollow cage-like structure.
It becomes exactly zero, so long as certain conditions are met. Namely no strong external magnetic fields. Some superconducting materials exhibit a transition region in between super- and normal-conducting modes, although resistance here is still very close to 0; crossing the critical temperature is still accompanied by a discontinuous drop in resistance.