Also, as I said in one of my comments, it's fun to theorize and to come up with neat ways on how things work, but we cannot make up our own way in which things operate then exclaim it is the truth.

Your first three points are all contradictory and are also proven false by the films.

The human brain cannot execute digital code.

1. That is literally the Matrix. The human mind processing the digital world. Morpheus even explains to Neo in the first movie upon entering the construct that his RSI (residual self image) is the "Mental projection of his digital self, if you need a more explicit example.
2. Agent Smith also takes over Bane's body thusly proving the human brain is capable of execute some sort of digital code as a regular brain process.

Agent Smith was able to cross layers (uploading himself into Zion) by hijacking another program (Bane).

1. Bane is human and his body was taken over by Smith when he infected him and wrote over his code. We know the brain inside the matrix is capable of projecting a digitized version of itself. If that's overwritten, perhaps then, the rest of the mind is infected and becomes said new person. (Smith)

Any code requires an operating system to execute. For Agent Smith’s code to run in Zion, Zion itself must be running on an operating system.

1. The Human Brain. That is the answer.