Hi, I'm wondering as to how games integrate story and sequence of events into their engine? What I mean is how do you tell your engine that when character reaches x stage of the map, for example initiate a fire and send 3 enemies of type x to that location? Where and how does this logic leave? Also how can I tell when the level is finished based up the completion of x, y and z; what if from level to level the number of tasks change or in certain levels you have no tasks other than wondering around for x number of minutes?

You might want to take a look at some articles on Game Scripting.

Game scripting is the best approach to go with, and it is also a pretty general topic. If you look at some open-source games that have a good amount of gameplay content in it such as battles, different maps/areas, and other scripted events, you will notice that the game will have a large amount of text files in certain directories that can have just about any extension (if any) imaginable to them! You should also take up this approach, however be warned, others will be able to edit these files... If you do not want others to edit your game's scripts, you could 'serialize' them by compressing them into a binary format using your own converter software (very, very easy to write). Then, all that's left is to make your game able to read this binary format which is also just as easy.