So, to start, HP is not an exact measure of if they are alive. It is more of a general idea of how much more they can take. For instance, if they are stabbed in the throat, unless they can somehow survive it normally, they will still die. If it drops to zero, it does mean that they are dead, however, someone cannot just remove another's HP and then they will drop dead. The zero just means that they have no life left in them to measure, or something is preventing the measurement.
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Mana is similar, but not the same. If one runs out of mana, they will become exhausted and probably pass out. However, they can continue to draw on mana past their capacity at the expense of possible harm and a source to draw from.
I know the first few chapters seem rushed, but that is because those were ones I just wanted to use to give a bit of insight into future events. Within the next few chapters it will slow down a bit.
And with that, have a great day!