Maybe, but probably not. The code requirements are far different for a house than a shed. Plus the structural material (2x4s, etc) may not be sufficient.
Sure, but to bring it up to code - foundation and framing structural calcs, plumbing, electrical, insulation, you might as well tear it down and have an architect design a house that looks like a shed.
Every location has different codes, but it's unlikely, since sheds are usually pretty flimsy.
Is it legal (city building codes and what not) to turn a shed into a full-time living space?