Bringing images into alignment
For 2D cameras, you can't.  There's a reason why the matrices only give constraints that let you say that point p in i1 must lie on line l in i2 -- that's because that's all you can say.

In particular, for a particular point p in image i1, with 2D cameras, you don't know the depth of the corresponding object.  The depth affects where it appears in image i2, so without knowing the depth, you can't know which pixel in i2 corresponds to p.  If the object is very close, then there might be a very large offset; if the object is very far away, there might be a very small offset.

This is in fact the basis of binocular vision.  Some 3D sensing methods work by somehow finding the correspondence using various heuristics (e.g., image similarity metrics), and then using this to infer the depth of the object.

So, the intrinsic and extrinsic parameters are not enough to uniquely deduce the correspondence, if both cameras are 2D cameras.  With a 3D camera, this problem can be solved.