I have another theory that's a variation of one of the already posted.
I think that there's a nested matrix. This means that zion and all of the "really human stuff" is actually the real matrix and what we consider (I mean we, the audience) the matrix it's just a diversion to keep people busy, never realizing that they're actually pluged while they think they're free. This could explain why Neo had his powers outside the ship.
I'm sure that this lets a lot of holes to fill on other things so I'll read to see which ones you post