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Just before any player would recieve priority, the game checks for any State Based Actions. Among other things, SBAs look for players with 0 or less life. If such a player is found, then (s)he is 'killed' immediately. In a duel, this means the game is over, and anything that could still happen just plain doesn't.

As for multiplayer games:
[quote]800.4a When a player leaves the game, all objects (see rule 109) owned by that player leave the game, any effects which give that player control of any objects or players end, and all spells and abilities controlled by that player on the stack cease to exist. Then, if there are any objects still controlled by that player, those objects are exiled. This is not a state-based action. It happens as soon as the player leaves the game. If the player who left the game had priority at the time he or she left, priority passes to the next player in turn order who’s still in the game.[/quote]

All combat damage happens during the combat damage step. Combat damage happens as a speciall action at the beginning of the combat damage step, and does not use the stack.

And to answer your last question, both players get priority in every step of a turn except the untap and clean-up steps. Some steps have special actions that can/need to happen before a player gets priority (declare attackers or blockers, or draw a card for example), but each player will get priority in each step.

I hope this clears everything up for you :)

A draw is very rare in magic because of how the stack resolves. You only get draws when playing with a time limit like they do at tournaments and time runs out before either side wins.

So like efinmiller said, you die and your lightning bolt never resolves so the other guy isn't affected.

Just to nitpick, if I may. Running out of time isn't the only way to draw a game. There can also be a draw if both players loose simultaniously, if the game enters an infinite loop of mandatory actions, if an effect says the game is a draw, or if all players agree to draw the game.