as far as starting with a dead battery (assuming you don't have a kickstart [I think they start with a dead battery]) you'd have to bump or pop start it.
Just like a manual car, get it rolling in gear with the clutch pushed in then pop the clutch, or release it quickly. Cars are a bit easier than bikes because there is more weight. With my bike (the seca) it took me pushing it at full sprint, down a steep hill then hopping on it and coasting till it gets to around 10 MPH then popping the clutch in second.
As far as the alternator question, I don't have the slightest clue.
and running the bike without a battery all together. ... maybe if you connect the positive and negative terminals (where they would connect to the battery) together, effectivly completing the circuit a dead battery would normally complete, and pop start like I said above but I wouldn't try that for fear of frying electrics.